sercurity light stuck on... help

I just purchased a 94 Z w/ 115K and the security light is stuck on. The car starts and I can drive it anywhere, but the light is on. I cleaned the pellet in the key, but that didn't help. Is there a way I can fix this myself without taking it to the dealer?

try un doing the battery terminals and let it set for 10 minutes and hook the up. sometimes that works.