How familiar are you with the 'innards' of Windows?
I'm fortunate enough to be able to build, fix, and clean up computers that are 'hopeless'. The problem these days is that NONE, and I do mean NONE, of the software vendors out there perform a 'complete' clean up when removing their software from your computer via normal means, such as the "programs and features" screen in the control panel of Windows.
=IF= you are comfortable deleting the contents of folders and even complete folders, AND know all the hidden folders that Adobe products use such as Users/<your ID>/AppDta/Local/Adobe, AND, if you have several Adobe products, know which folders within THAT one to delete, then have at it. And =IF= you really feel lucky, carefully extricate Adobe from your registry. Of course, have a FULL BACKUP of the drive that controls Windows. It's very possible to screw things up enough that the computer won't boot! Knowing how to restore from a previous version of the registry can be very helpful!
These days, software authors seem to have little idea of the hundreds, even thousands of entries they create in the registry for a single product. I recently tried to update the device driver for my video card and what should have been an uncompressed 1-2K file was a 488Meg exe file that expanded into 4GIG of space on my SSD! These days, giving the user =options= of selectively installing products gets more rare every day. The same 'device driver plus' wasn't even 'nice' enough to show up in the 'programs and features' screen, when it installed 4 different products and 24 different language files! Even with automated registry cleanup software, it still took me more than 3 hours of 'fixing' to get rid of the useless trash. I just installed a new name-brand scanner today, and it wasn't even 'polite enough' to offer -any- installation options! One can only click on 'agree' to the license and away it goes! I haven't even begun to find out how much useless garbage it put on my computer.
Then there's the 'free software' for <whatever> that will install various added toolbars, security software, advertising software, even anti-virus software if you choose the 'standard' installation they offer. They'll even replace your internet browser and search engine if you let them! All with your implied permission by choosing 'standard installation'. How user friendly can they get? In short, the reason the once super-fast computer has slowed down is all the 'free garbage' that comes along with something useful.
As a suggestion, perhaps the Adobe chat rep can do a remote-control of your computer and do some judicious 'cleaning' to allow a clean installation of the paid software to operate. Believe it or not, it could also be something as simple as modifying a single parameter in the registry...IF the rep really knows his stuff!