Car won't start....HELP!!!

I have a 94 GT vert. I drove it home from work last night and stopped to get my mail. I got back in my car and tried to start it and nothing happened. I turned the key to on and the gauges light up and everything works fine. Then I turn the key to start and everything just dies. The interior lights go off, the gauges turn off, everything. After a couple of seconds everything come back on. I tried it again and the same thing happens. At first I thought that it might just be the battery, but jumping it doesn't change anything. The car had an old "security system" on it when I bought it a year ago. I don't know if this could have changed anything, but the alarm is pretty old and I believe that is is Crimestopper.

Please help, I haven't really had a chance to look at everything, since it was dark when I got home last night. Any suggestions would be greatly appreciated!!!!!

Thanks Jeff

Problem fixed

Thanks for the help guys..... I found that one of the battery cables was not getting a good connection with the battery. I just took the cable off and cleaned it, then put it back on and it worked just fine.

Thanks again for the help
Jeff