A few games have a freeze issue..lego star wars for instance.
Some games, GTA's ect must have the time set, the default 6th of june 00.00 of dashes will not do, the time chip in the xbox must be set, note the time chip will lose it's setting after @4 hours without power.
It could also be the cache files are corrupt, find and delete the e:\cache folder, it will be recreated automatically when a game needs it, and also delete anything on x: y: z: drives.
Check the fan by putting your hand over the vent on the back and turning it on! At least it will rule the fan issue out. My mates fan use to come on at first then go off after a hour... so i lifted the top cover off and pressed the fan connection to the board with a plastic probe and the fan came on! Only perminant cure is to solder the connections straight to the board.
Machine has been running fine for over a year now! RESULT ;-0