Applications won't run for a variety of reasons. I have seen task manager refuse to run due to virus infection reasons... I believe that is part of the MyDoom series of viren that are out there running about.
I would open up your logs using compmgmt.msc, and take a look at your logs. See if there is anything strange lurking around in there. You should also backup your data files... if it boils down to be an OS issue, you will have to rebuild the system.
I hope you have rebooted the computer, and that this problem is still re-occurring. Rebooting the computer has solved this problem for me too. I also assume your virus defs are up to date.
If the problem is in taskmon.exe, directly replacing it would be a good idea. I could fire up my w2k box and email that program to you. But if the problems are with .dll's, then we have to find some sort of install program to deal with it.