Hi Jakin,
This is definitely too high a volt drop and it would appear you do have a problem on the board. I would suggest
1) With power applied quickly touch all the IC's, transistors etc on the board one after the other checking to see if any are getting excessively hot, simple but effective.
2) Checking all components between VCC and Gnd to make sure the correct values have been fitted or wrong component fitted i.e. a inductor instead of a cap, suprisingly easy to do if it is small surface mount components.
3) measuring the impedance between VCC and Gnd to see what you read. If there is a low reading then if you have a sensitive enough meter you can try to track down the faulty component by placing one probe on a gnd connection and then probing at various points on your VCC line as you get closer to the faulty componenet you should see a very small drop in impedance.
Another way to track down the fault is to isolate the supply to successive IC's then power the board, at the point that when power is supplied and the voltage stays constant the last IC you isolated would be the faulty one.
Hope this helps, keep me informed how you get on tracking this down.