If your Quicken was before 2010 you should have several files making up the data.
The main data file ends in .QDF. All Quicken versions prior to QW2010 store your data in a series of files all sharing the same filename but with different extensions like - .QDF .IDX, .QEL, .QPH and all 4 of those files were rolled into a single-file .QDF starting in 2010.
If you need to convert to a newer version you need to go through one or more intermediate versions. If you don't want to download or import transactions you can stick with Quicken 2013. I'm using 2013. It's the last good version before they started requiring an ID.
You can download 2013 for free using this how to convert article. It’s under Converting from Quicken 2004-2009.
But if v2013 couldn't open your data it must be from a newer version.