If you haven't trashed the first kegerator yet, I think I might have some insight into the problem. Most of the refrigerators (and, I assume kegerators) these days use a start capacitor/relay to start the compressor; and they are NOTORIOUS for failing. I have two newer french door refrigerators as well as an older one that is the kegerator; BOTH of the french door fridges (one is 10 years old, the other about 5) have had failed capacitors. Amazon sells an item called a 3-in-1 start capacitor for about $10-12 bucks, manufactured by Supco; I have them in both of the french door refrigerators (one is my ferment fridge) and they've never had a problem since. The older fridge has had one for over 2 years, works just great. If you do decide to go this route, and your kegerator compressor is 1/5 HP, I have an extra one you can have for shipping; they make two, the 810 is for smaller refrigerators (like dorm fridges, this is the one I have an extra of), and the 410 is for your standard larger refrigerator; I forget the HP rating.
Also, one other thing you can try; how long did you leave the kegerator unplugged before turning it back on? Compressors can take up to 4 hours to return back to equalized pressure of the refrigerant, otherwise they will not start.