Graphics card for thinkpad t60

No, you won't be able to change the GPU because it is not a discrete card.

Firstly it's not your graphic card's fault. Graphic cards are not responsible for video playback duties (modern ones do have a hand, but your's is not one of them). Does the video become choppy while you arfe watching it online? Then you'r buffering speed is not fast enough (due to a slow internet connection). Also update you FLASH version. If you'r having trouble playing them back after downloading them, then you should get the latest codecs for whatever media player using for playback.
And jbakerlent is right. You cannot change your gpu in any case ...