2001 New to me Cavalier

I bought a 2001 Cavalier at the auction last week. It runs well, but we've got one small problem, no lights. Here's what happens:
1. Start up the car, put it in gear, daytime running lights(DRL) come on, no problem.Turn on the lights and the DRL goes out. No headlights either
2. Car drives fine. DRL is on, yellow side lights are on but if you turn on the lights, the front lights go off but I do have tail lights.
3. About the 3rd time you start up the car, the DRL indicator flashes quickly on the panel, the service light (NOT the check engine) light comes on and the DRL's go out.

Went to AutoZone to have the service light read and it came back with a P1621 Error - something like Immobilizer codes does not match.
Roommate and the guy @ Autozone thinks it's a bad key but I'm not sure. Could it be the DRL Relay in the fuse box going bad? The car has manual locks and windows so I can's see it having a theft system on it. Anybody else have a guess??

Update - went to Napa and got the DRL Relay that sits in the fuse box. No change..no headlights. Help!!!!!!!!!!!!!!!!!!!!!!!

i seriously doubt its the relay, this is a long shot but it could just be that your headlights are dead, at least the low beam part of both of them, cuz the drl's use the high beam bulbs, just at a lower voltage, and whenever one of your exterior lights goes out, (like a headlight) that yellow drl light does something, i dont remember what though (i think it just flashes)