Trying to retrieve information from Quicken 2007 .qdfm files. Have new Quicken.

Quicken Mac should definitely import your Quicken 2007 data file(s). In Quicken Mac, go to File > New and on the Getting Started page, select Start from a Quicken 2007 data file; select the data file you want to convert, and it should process your data file into the current format. You can repeat this for as many different Quicken 2007 data files as you wish to convert.

If this isn't working, please give details about exactly what you are seeing and any error messages you're receiving. 

Some additional questions... Are you now on a different computer from the one one which you ran Quicken 2007? Do you still have that computer/can you still run Quicken 2007? What version of macOS is on your current computer? How exactly did you move the file(s) from the old computer to the new computer.

The problem you mention often occurs when the file was copied via a non-Mac formatted disk, such as a flash drive formatted for Windows. 

@Alewitz  Let me address a few of the things in your post to focus on the right things...

Quicken vs. Intuit is really irrelevant. The modern Quicken Mac was born in 2014 when Quicken was still part of Intuit, and from that moment they began telling Quicken for Mac users that their support for Quicken 2007 would continue as they worked to add features to the new program, but that it would end in the not-too-distant future. Indeed, support for Quicken 2007 was terminated two years later when Quicken 2017 was released. But Quicken 2007 continued to work -- and still works today -- on macOS up through Mojave. It cannot run on Catalina or Big Sur because the latest Apple operating systems only run 64-bit applications, and Quicken 2007 is a 32-bit application. In the interim, Intuit sold off Quicken in early 2016, but that really has nothing to to with support or the progression of the old and new programs. So let's leave the corporate issue aside, as well as any hope/expectation that Quicken will provide support for the old program five years after they ended support for it.

So let's focus more on the issue at hand. You wrote...
As mentioned above, your move to Big Sur is what made Quicken 2007 unusable. The end of old 32-bit applications running on macOS has been extensively written about over the past three years, in the lead-up to and release of macOS Catalina. I'm sorry if you were unaware of this from either the Mac side of things or the Quicken side of things, but it's certainly been extensively documented for years.

Other than that, there's no update to macOS which renders Quicken 2007 or its file unusable. I'm still running macOS Mojave on one of my Macs, and even though I run modern Quicken Mac on that computer, I can still launch and run Quicken 2007 on that computer, and it reads my Quicken 2007 data files without issue.

The format of the Quicken 2007 database is not just proprietary, but apparently very complex and convoluted as it evolved over the decades. Even Quicken had a hard time extracting data from it in order to move to the modern Quicken; the import routine uses a complex exporter which is actually a stripped down version of Quicken 2007 to get data out into an intermediate format which can then be imported into modern Quicken Mac. You will not be able to pull out chunks of data into Excel or Word or another program. the database use in Quicken 2007 was developed back in the early years of the Mac and was optimized for speed and compactness, so the data isn't sitting in the file as blocks of text which can be pulled into other programs.

So let's narrow in again on your Quicken 2007 data files and whether there's any way to rescue them.

The missing resource fork error indicates the file wasn't copied in the right way, so let's revisit that. You said "The HD was migrated from another powerbook several months ago" and "Quicken 2007 was working fine up until at least a few weeks ago". There's something I may not be understanding in the sequence of events...

You moved data from your old Powerbook to the newer Powerbook awhile back, but the new Powerbook was running macOS Mojave or an older operating system? So you continued to run Quicken 2007 on the new Powerbook? Then a few weeks ago, you upgraded the macOS on the newer Powerbook to Big Surprise and discovered Quicken couldn't launch? Is that correct?

I don't think it's relevant, but out of curiosity, how did you move your data from the old Powermac to the newer one? From what you've said, it probably shouldn't matter if you were able to successfully run Quicken 2007 on the newer Powerbook after the transition.

Do you still have the old Powerbook, or is that gone now?

You then mention that you have an older iMac, and that it also can't read the Quicken 2007 data files. Did you try this by copying the data files on your current Powerbook to the iMac after you upgraded the Powerbook to Big Sur and found Quicken didn't work?

And now the $64,000 question, which I suspect you've already answered by not mentioning it: do you have any backups of either your old Powerbook or the current Powerbook from prior to the Big Sur upgrade?

(If not, this is a subject for another day, but as this situation illustrates, it's crucial for every Mac user to have at least one, and ideal multiple, types of backup to protect all your valuable data. Time Machine is the easiest to use; buy a $100 external hard drive, plug it in, the Mac will ask if you want to use it for a Time Machine backup, say yes, and it does the rest. Since you're backup up a laptop computer, you can dismount the Time Machine drive and disconnect it, and just plug it in every few days or once a week to let it automatically back things up. Another option is an online backup service such as iDrive or Backblaze. This may have a higher cost over time since you pay a monthly or annual fee, but there's no hardware to hook up, and it will back up your Mac wherever you're using it.)

Back to the matter at hand... I am not aware of any reason that an upgrade to Big Sur would, in and of itself, damage your old Quicken 2007 data files. Although the use of resource forks in Mac data files has long ago been deprecated, I believe all versions of macOS will still properly read old files with resource forks. And the current Quicken Mac will indeed still import Quicken 2007 data files. So I'm not clear from your description of the problem where/how your Quicken 2007 data files were damaged or data was lost. I haven't seen any other reports of such a problem on this forum. Clearly, the best path toward resolution would be if you can locate any old copies of your data file(s) from the old Powerbook -- even if it's a few months out of date -- or backed up prior to your upgrade to Big Sur.

First: .qdfm files are "packages" files, so there's nothing wrong with that. It can't identify the file as belonging to Quicken 2007 on the Mac running Big Sure, because that Mac doesn't know about Quicken 2007. I'm not sure why some of the files are labeled as MP3 Audio, but I wouldn't worry about it; it's just that that Mac doesn't know what these files are. 

Since you have Time Machine (yea!) on the Powerbook predating these problems, I'd start there. You should be able to restore the Quicken 2007 data file from a month ago (or whenever you're sure you last used Quicken 2007 successfully). Without doing anything else to it, you should then be able to have modern Quicken Mac import that file. (Note that when you restore from Time Machine, it will default to installing the restored file in the same place and with the same name as an existing file. So before you restore, rename your existing Quicken 2007 data file -- even though it appears to be useless at this point. you always want to preserve every version of files when you're trying to recover from a problem, in case you need to go back to something later. Similarly, if you need to try restoring more than one file from Time Machine to go back further in time, rename the one currently on the Mac before restoring another file over it.)

The other option would be to try via the iMac. Since your iMac is running Sierra, then it will run Quicken 2007 without any need to install anything else. The key here would be seeing if you can restore a copy of your data file from Time Machine. Time Machine can be finicky about restoring files from other computers. Hold down the Option key when launching Time Machine from the menu bar, so that "Enter Time Machine" on the dropdown menu is replaced by Browse Other Backup Disks. Then try to restore a Quicken 2007 data file or backup from prior to when you had these problems. You should just need to double-click on the restored data file to launch Quicken 2007. If you're successful with this, then we can talk about how to safely transfer the file to the newer Powerbook running Big Sur for import into Quicken 2007.