Before you go buying a mod chip, check your basics -- make sure all of the cables are secure (both internal and external), and test the hard drive, DVD drive and IDE cable. Make sure nothing is weird on the motherboard. If everything appears to be fine, you reassemble the Xbox and it still doesn't work, your TSOP is probably corrupt and you will need a mod chip.
If anyone else knows of any other problems that may cause this, please post them below.