That's actually quite true. The skull adds a good 3-6 db of gain to the signal. I used to have a Chevy that I could unlock from 50 feet away using that trick.
Testing the remote is easy. Just get a broadband RF preamplifier that works in the frequency range of the remote. Put a makeshift antenna on it. Then, couple the output of that RF preamp to your handy dandy RF spectrum analyzer. You should see a nice peak in the frequency range of your remote when you activate it. If you don't, looks like the remote's dead.
What, you're not a T.V. engineer too?
Okay.....
First, just open it up (if possible) and check for anything obvious such as broken solder joints.
I would also check to make sure your car hasn't "forgotten" the keychain. There is usually a way to program the car to use the remote, and it involves the car "learning" the signal from the remote. Check that angle out.
Good luck!
-tp