hmm, sounds similar to a problem i had on my old computer. i'd load the game and get to the main menu only to face a black screen with the menu music playing in the backround. i never really figured it out after reinstalling the game, getting the latest video drivers (i had a GF-FX5600), and doing a ton of system maintenance. in retrospect, i think the problem was probably with either the new firewall my Dad installed or with another program that my Dad finished installing at the same time.
basically, if you have a firewall other than the Windows Firewall running, see if you can find a log that lists the programs that its blocked from running. if you see 'swkotor.exe' (or swkotor2.exe in the case of TSL) as being blocked, then add the game to your list of allowed programs. if you can't find it, physically disconnect your computer from the internet (unplug whatever has you connected) and disable the firewall.
if that doesn't fix the problem, you may want to start doing some research to see exactly what's running on your computer. press the infamous 'Ctrl-Alt-Delete' key combo and pull up the task manager. under the 'Processes' tab is a list of all the programs that are running, both backround and foreground programs. then check out this handy program library (
http://www.sysinfo.org/startuplist.php) to find out exactly what's running. if you find anything suspicious, you might want to seriously consider looking into finding a way to shut them down.
also consider checking out this trial-based utility (
http://www.tune-up.com/info/lp/tuneup-utilities/?ap=1609) to help clean up your system. it has a ton of handy tools that are extremely useful to help get your computer running better in general.
otherwise, my solution to the problem was to simply get a new computer. anyways, i hope that helps out just a bit. :)