Allmost the same problem here. I can download Basecamp 452 and when the application launches from the install it works ok. Close it and I cannot open Basecamp. Windows registry error. I have tried all sorts, deleting short cut, delete the files, uninstall, run CCleaner, move files from x86 program files to program files etc. Only way I can get it to work is as follows. Download 7zip. This allows you to extract the files from the .exe folder. Once done look for either the BCMAIN or Bootstrapper.exe file. Click on this to start Basecamp. It will go through part of the install process but will launch. No idea why it does it. Windows 7 64 bit.
You can also try this. Back up your data, I can recommend WD Ultra Passport 2TB, excellent piece of kit. Reinstall Windows 7 from your CD drive. I will try this later on in the week. It will give the PC a new lease of life.