You're right: block heaters are really simple devices. The problem is either the heating element (they can burn out) or the cord.
It's more likely a damaged plug or cord, based on your description.
You can use a multimeter to test the cord's continuity. I'd recommend wiggling/bending it while doing this to see if you've got a partial/intermittent break.
If you don't have a multimeter, you could plug into a kill-a-watt and watch the current draw reading while doing the same thing (working the cord).
FYI, this thread may give you some ideas as well:
Kats heater FAILED AGAIN