Unusual problem. Obviously, it's an electrical issue. Either a dead short or a bad connection. I'd start by checking all the wires and connections from the battery pack to the receiver. If all of that checks out, replace the receiver.
That would tell you where the problem is without dropping a lot of money. If the new receiver does the same thing, you will have a spare receiver and know that the problem is in the transmitter.
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EDIT:
I'm starting to lean towards a transmitter issue. Normally, if power is lost the servos will just stop but the fact that they go full in one direction tells me they are being told to do that by the radio.