Yeah, you'll have to patch the games. Just follow the instructions in the second post of this thread and you should be fine. Since you have an Nvidia GPU the problems should be minimal.
As far as your screen resolution is concerned, check out the Widescreen Gaming Forum. Their UniWS utility will work on KotOR 1, and there is a patcher by Squ1zZy for KotOR 2. Don't forget the HUD files for both games.
"They should rename the team to the Washington Government Sucks. Put Obama on the helmet. Line the entire walls of the stadium with the actual text of the ACA.
Fix their home team score on the board to the debt clock, they can win every game 17,000,000,000,000 to 24. Losing team gets taxed by the IRS 100%, then droned."