Just a couple of notes, since they may be helpful down the road.
First off, the OEM license terms were changed before 7 came out, so odds are whomever sold that copy to you, shouldn't have.
Second, save for a very select few programs, the 64-bit version of Windows has full backwards compatibility with 32-bit programs. There was no need to waste that last half GB of RAM. I'm not sure if the OEM setup is like the upgrade discs I got, where there's both the 32 and 64-bit versions included, but since there's a good chance your issue will result in having to reinstall, it'd be a good chance to move to 64-bit if it is. The only thing 64-bit Windows doesn't have, is 16-bit capabilities, but then Win2K had rather poor and limited 16-bit support anyway, and those programs should have been phased out 10-12 years ago.
It honestly sounds like your issue is one of malware damage. You may have been somewhat protected by the age of Win2K in the past. Malware may have simply failed to work because no one bothered to make sure it did work on Win2K. You might be able to fix it via the registry, but more times than not people make things worse when they start spelunking around in there.
Also, you haven't run any kind of registry cleaner/fixer programs have you? If not, be sure to keep it that way. They will usually create more problems than they solve, and there's no easy way to recover from any damage they do.
Since it sounds like your install is still fairly new, I would simply blow it away and start fresh. A bit of a pain, yes, but usually in cases like yours you can either rip the band-aid off now... Or you can keep on keeping on, without any idea of how long it may take to restore full functionality, with no guarantee that is even possible. Formatting has a known quantity of time you'll need to invest, whereas trying to fix an issue could be a matter of minutes, hours, days, weeks, months, even years depending on how stubborn you are. Usually it's faster and easier to just spend 2-3 hours formatting and reinstalling.
And one final thing. You don't have any blank discs in the DVD drives by any chance do you? And you don't have any packet writing (CD as a floppy) software installed like Nero InCD or Roxio DirectCD? That could certainly explain your reported issue. Especially if they're older versions.