I had the same problem. Here's how I got around it:
1) Uninstall KOTOR completely.
2) Insert the 1st disc, but DON'T run the installer from the autorun launcher.
3) Go Explore the disc, and manually run Setup.exe IN COMPATIBILITY MODE for
WinXP. (right-click, properties, compatibility)
4) After installing, make sure swkotor.exe is running in Compatibility mode
for XP AND is being run as an administrator. (right-click, properties,
compatibility). Then run it either through the launcher or by
double-clicking on swkotor.exe.
5) If you get an error about Securom (every so often), just run it again.