Hi, let me start by saying I never used Kaspersky, so it's just a shot, BUT (!) an antivirus program is different from an anti-spyware program, so having both makes sense.
Kaspersky won't warn you about spyware infections,
since spyware does not equal virus. That's why one program says the PC is fine, the other says it found an infection. Kaspersky was never intended to look for spyware in the first place, it's an anti-VIRUS!
Oh and by the way, Ad-Aware is a better program than the built-in spyware protection from Vista (shit*cough*), so I suggest you get Ad-Aware (it's free), run a scan and free your PC from mal-/ad-/spyware
Again, this is just my guess.