freezed up discs

since i bought my xbox 360 i have had alot of problems with games i have bought  minor scratches (mostly used games) seem to have alot of problems in my 360.  like dead or alive i got it used  and the game loads and all  but you can tell there is a problem right from the  team ninja advertisement at the start when it loads.

then it just gets worse i choose my character and  start playing and blam the music stops game still plays but then next round blank screen..

anyone have any ideas on quick fixes to repairing discs.

i have heard toothpaste  remove minor scratches.

but before i try anything i would like to hear from other gamers who have had problems with games loading