Problem solved, possibly.

I finally figured out that the incorrect account key belonged to another person who had installed BOINC on both this computer (years ago) and on the second computer (months ago).

Are you the owner of that "other persons" computers now, and it's the same computers that you are using?

Loose thoughts:
- The account key isn't stored in Windows registry. You can check this yourself at HKEY_LOCAL_MACHINE\SOFTWARE\Space Sciences Laboratory, U.C. Berkeley and HKEY_CURRENT_USER\SOFTWARE\Space Sciences Laboratory, U.C. Berkeley
- I had already explained how to log in with the account key in this post, so no "trial and error" needed.
- Uninstalling BOINC merely removes the BOINC program files at the BOINC Programs install directory (default C:\Program Files\BOINC)
- Neither you nor your computer helper thought about asking any of the above here? I then wonder why not, are we not here to help, have I not sent you help? Or have you searched on the internet for answers? BOINC has been 18 years in development, surely someone would've written something down about basic things like this?

I'm finding it hard, from my knowledge of how BOINC is designed to work, to see how this solution could relate back to the original problem. I've had a look through my own registry, and in all the - multitude of - entries, I haven't seen a single one which relates to a user account key. Those are all stored in the files in the BOINC data folder.

The data folder - by design - does not get deleted when the BOINC programs are uninstalled. This is to allow for version upgrades: an upgrade requires the removal of the old version, and its replacement by the files for the new version. The plan is for the user's data to remain unchanged during this process, even to the extent of keeping part-processed work intact, and restarting it at the exact point the previous version left it at.

All of which is a long way of saying that this may be a temporary fix - don't be too disheartened if the problem returns in the future.

One thing that hasn't been discussed so far is the potential role of project servers in all this. The BOINC server code contains tools which try to re-unite a lost computer with its owner's account. From memory, it considers things like hardware configuration and IP address - there may be others. Might it be a possibility that one of the projects you're attached to is using a buggy version of that code? It would be a hard one to track down, but the first step would be to make a note of the computer's 'HostID' or 'Computer ID' at each of the projects it is attached to - it will be different in each case. Check it locally first ('Properties' button on the 'Projects' tab, BOINC Manager, Advanced view). Then check that the same number is used on your own account on each project's web site.

Then, if it changes again to the old account again in the future, check the list of HostIDs again. I would expect that at least one - hopefully just one - will also have changed. Go to the project web page, and see what account the new HostID is attached to. That would give us some clues to work with.

• I add the Rosetta@home project in BOINC Manager
  
• Project is added, and associated with my account ID, 255 (illustrative)
  
• Project runs - but after some time the account ID in the xml config files changes to an incorrect value, 133
  
• I remove the project and re-add it in BOINC Manager
  
• Project is added, and associated with my correct account ID, 255
  
• Project runs - but after some time the account ID changes back to 133
  
• repeat, etc.