Since yesterday, whenever I open Windows XP Task Manager, the program will shutdown by itself. I can't localize the problem.

First thought that comes to mind is see if your ESC key is sticking by pressing and wiggling it several times.

Second thought that comes to mind is that the computer is infected with malware that is closing the Task Manager process in order to thwart attempts to identify and remove it. Update your security software or antivirus signatures and run a full system scan.

I also suspect some spyware/malware...

Download and run SmitFraudFix (Google it)
Then install an anti virus if you haven't yet.

:)