The game just won't start at all. Please use simple language when helping me. I'm not a computer guy.
There are a couple of things you can try:
1) In the folder where you installed Knights of the Old Republic (mine is located at C:\Games\Steam\SteamApps\common\swkotor - your install location will be whatever folder you selected in the GOG installer) you'll find a file called swkotor.ini. If you don't see the .ini portion of the file's name, look for an icon that resembles a page with a gear on it called swkotor.
2) Open the file in Notepad or your text editor of choice.
3) Look in the section headed with [Graphics Options]. In that section may be a line - Disable Vertex Buffer Objects=1
4) If you don't see that line (I believe it's in the file provided by GOG though), than copy it in to the file at the end of that section (before the line that says [Autopause Options]
5) If the movies aren't showing when you open the game, you may want to add the line Disable Movies=1 at the end of the section labeled [Game Options].
And the usual - make sure drivers are up to date, etc. Hope this helps. =)