When setting up an eBill, is there any way to find out why it rejects a legitimate login?

If you haven't done so already, I'd say it's time to call Quicken Support on the phone and request help.  Let them do a screen share session with you to review the situation on your computer, to determine the nature of the problem and to figure out how to fix it.

Quicken Support:

• To contact Quicken Support, please use this link only:
  https://www.quicken.com/support#contact-support  and select Chat or Phone support.
  Phone support is only available during posted business hours. The phone number can be found at this website.

• To start Chat or see the support phone number, your browser must allow popup windows from https://www.quicken.com

• If you are eligible for Premium Support (purchased separately or included as part of your subscription to Quicken 2018+ Premier or HB&R) call the number that can be found at the top of your My Account page at https://www.quicken.com/my-account  (US) or https://www.quicken.com/canada/my-account (Canada) next to "Quicken Premium Support"  when you log in with your Quicken ID.

• Other links or phone numbers found elsewhere on the Internet, even in some posts or emails received from other Community members, may not be from Quicken or may not be up-to-date. Use those at your own risk.

• Unlike other so-called "Quicken support providers", the real Quicken Support is free for all currently supported versions.