98 Cavalier Z-24 (Won't start or turn)

My car's just under 100K, and I replaced the battery about 4 months ago. I turned the car off today and when I tried using the door lock button, nothing happened. I've had a similar problem in the past when I've turned the car off and removed the key quickly so I put the key back in, no dice. I try starting the car up, nothing, the endine won't even crank.

My friend came over to give me a jump and still nothing. Then I noticed an odd clicking sound. After testing a few things out the sound was coming from around my glove compartment and that if I pushed the door lock buttons or turned the windshield wipers to an on position, the cliking stopped. This sound was also only happening when the key was in the initial position. (I.E. When I tried starting the engine, or turned it to the auxillery position the clicking also stopped.)

Any ideas as to what this is?