You've done a bit of tinkering, so you may have added a bit more to the mess.
But go to C://ProgramFile(x86)/Adobe and just delete the Adobe Premiere Elements 7.0 folder.
Then run CCleaner (a free download) to clean up the junk it left in your registry.
If you really want to be thorough, enable your Folder Options to Show Hidden Files and then go to C://ProgramData/Adobe/Premiere Elements and delete the 7.0 folder from there too.
I can't imagine that Premiere Elements 7 did something to Windows Backup. They don't really live in the same world. But throwing out the program files and running CCleaner should pretty much remove the program from your system so that, if you'd like to, you can reinstall it and, if you'd like, do a formal uninstallation.
That's a good suggestion Steve. I hadn't thought at all about CCleaner. Thank you....
I'll be upgrading to Windows 10 fairly soon (while it's still free), so as of yesterday I've also started thinking about another option which would be to install Windows 10 on a completely wiped-clean hard drive rather than loading it on top of all the years of garbage that's accumulated in my Windows 7 system. Reinstalling everything from backup would be a lot more work, but it would result in a far more reliable system in the long term and probably avoid a lot of other problems as well.
I'm not sure which way I'll go yet.
It's more work -- but I think that would be a very wise way to go, Terry!