I hade the same trouble before (and when i finaly made it out i just got a 100 new problems). Anyway I started looking around and i found that there is 2 way to advance.
1: you play on the hard drave or cd untill you get to right before that cylinder droid is about to blow. If you played hard drive save that game, reboot the x-box and start the game with the cd. Now load the save and play trought the blow up and save afterwards then you can keep on playing on your hd.
2:the other contains edeting a file (no worries if a noob like me could do it so can you). There is a file named "swdirsXbox.ini" in your Kotor II direction and this is how it looks original.
Now as you problebly notice every direction are pointing to the dvd drive. (aka the play disk). If you just edit this so it will fitt in with your Kotor II direction
HD0=f:\games\Star Wars KotOR II
OVERRIDE=f:\games\Star Wars KotOR II\Override
ERRORTEX=f:\games\Star Wars KotOR II\Errortex
MODULES=f:\games\Star Wars KotOR II\Modules
LOCALVAULT=f:\games\Star Wars KotOR II\LocalVault
DMVAULT=f:\games\Star Wars KotOR II\DMVault
SERVERVAULT=f:\games\Star Wars KotOR II\ServerVault
STREAMMUSIC=f:\games\Star Wars KotOR II\STREAMMusic
TEXTUREPACKS=f:\games\Star Wars KotOR II\texturepacks
STREAMWAVES=f:\games\Star Wars KotOR II\StreamWaves
LIPS=f:\games\Star Wars KotOR II\Lips
Now this worked fine for me hoppes it will work for you.