Security / Fuse Relay

My 97 Camaro will not start.  I'm parked up hill (everything working fine) and when I came back, it wouldn't start.  The first two times I tried, the security icon was light for a few minutes after the failed attempt to start.  I, like the manual said, waited a few minutes until the icon diminished and tried again (and after making sure my key was okay).  
I tried turning the key a third time and the security icon didn't stay lit.  The interior lights, the dash, the radio, the headlamps, everything work fine, but the car won't start.  Everytime I turn the key, there isn't an audible clicking (like the alternator trying to click over, no sound at all), so I thought there might be a fuse issue.  
I checked all the fuses and they're all fine.  I buddy helped me listened to anything strange and everytime I tried, he heard a little clicking coming from the Fuse Relay for the ABS / LAMPS, but the head lamps work just fine.  Since the car won't start, I cannot check the ABS and since I'm facing up hill, parallel parked in downtown Austin, so I don't know (any suggestions?).