I agree it seems like a tough problem. Sorry I can’t give a ‘magic’ solution, but sometimes it helps to share!
The only things I know of that affect opacity are:
the Opacity control on the Layer
the Fade control on the Brush
the Diameter and Hardness settings on the Brush (these don’t technically affect opacity but they can give results that look like reduced opacity)
It would seem that you have eliminated these possibilities. Another error that can give rise to something that looks like an opacity problem is if you have accidentally gione into Quick Mask mode without realising it. However, this too would seem to be eliminated by the steps you’ve taken.
After various Google searches, the best set of hits seemed to come from these search terms: “Photoshop Elements troubleshooting”, and there are many, many pages there to look at. Who knows, maybe you’ll find something.
I agree that the re-install should have fixed the problem, but alas! it didn’t. The next suspicion I would have, if I were in your shoes, would be that for some reason the ‘comprehensive delete / install as new’ cycle wasn’t achieving what you wanted it to. It seems clear that your original copy of Elements, as installed on your machine, developed some weird glitch affecting brush opacity, and that the legacy of this problem is carried forward to each new install.
This can happen with software (my copy of Word has a similar problem, although thankfully a trivial one that doesn’t stop me working). In some cases, the attempt to ‘delete’ the software doesn’t actually delete it from the machine, as such; it simply wipes the top-level access you have to some .exe. files and makes the room they occupy on your hard disk available for writing over. But they still exist on your drive. When you re-install, if these files haven’t been erased in the mean time, the software ‘sees’ that these .exe files are still lying around, and so it doesn’t bother to install fresh versions over them. In other cases, the software writes certain changes into the deep, dark and (largely) inaccessible bowels of your system registry, and when the software is deleted these registry entries remain behind, and are sufficient to allow the bug to survive from one install to the next, like a poltergeist that meets each new occupants of a house.
Both of these types of problems are solvable, but in general you’ll need someone with more technical know-how who knows how to do a ‘root and branch’ deletion of the software, including possibly some surgery on your system registry.
One last point… if you haven’t already, it may be worth trying a ‘delete / re-install’ where you change all the default file names and file addresses during the install procedure, eg if the install dialogue says 'I’m now going to write this file t oyour hard drive as ‘C:\elements\Main.exe’ is this OK, you exercise your option to stash it in a completely different directory with a completely different name. There is a slim chance this might help, because sometimes these annoying ‘legacy bugs’ are glued to a specific file name or location on your FAT / file tree.