PSAPI.DLL is a legitimate file, and should (very likely) be on your machine. You could try copying it from another machine.
It's probably caused by some program that is automatically triggered when you logon. Have a look in the Startup program group, try running things in there to see if its one of them.
I found multiple versions of this file on my computer (Aug 1996 & Aug 2004), I corrected the problem by renaming all old versions (previous to 2004) to Psapi.old.dll.