Well, based on a lot of frustrated posts on the DC Forum, a lot of SP and MP gamers have had problems running PK on laptops with integrated graphics cards (namely Intel). The reason for this is that Intel do not support T&L (transform and lighting) required for many DirectX games.

http://www.dreamcatchergames.com/forums/showthread.php?t=24937&highlight=intel

Since what PK requires is T&L hardware support, to get around this, all you need to do is emulate that support in software. Since it doesnt use it much, you do not get much drop in performance.

3DAnalyze made by TOMMTI Systems. You can download that HERE. Their website is here http://www.tommti-systems.de/start.html

Download it, unzip it (basically run it), then run the App (3DAnalyze.exe) and you should see something like this:

Firstly select the Painkiller.exe, then tick the Emulate HW TnL caps box, then click Run.

There are other options of running in a Window etc. but you can try those out for yourselves.