Yes, unfortunately, programs installed on another hard drive won't be "installed" when you reformat and install windows again.
The problem is that all of the program's information are stored in the windows registry. While the program's information are still on a separate hard disk, Windows won't know where to look for dll's and other files about the program until they are re-installed (and put back into the registry).
It's odd that the self-diagnostics just restarted the computer. I've never seen that before (and I've been doing this since I was 8 years old, now 27). Of course, I haven't had many hard drives fail with that brand. WD and Maxtor are another story).
I've found that running diagnostics and having the computer reboot or do funky things while installing an OS can also point at a bad CPU, but not always. It's a hard thing to diagnose. To find out fully, it usually takes diagnosing each part individually with a known working system, or working with a bare-bones system and working your way up.
Anyway, hopefully you'll be able to get Windows installed again and all of your programs working properly. As for the defunct drive, you might be able to hook that up to an external hard drive reader of some sort and copy any files that you may need from it if it is in fact going bad. This won't restore your programs, but at least your docs, mail, internet favorites etc.
Good luck, and let us know if we can help you any further!
