i have seen many related starting issues for this model, with few verified solutions.
i would try to walk thru these 3 steps
1, is to reset/re"learn" your key, after a dead battery issue
http://pcmperformance.com/programming_files/GM_VATS_RELEARN_PROCEDURE.pdf
2. verify that you are NOT using a copied key to allow the car to "warm up" unattended, and then carrying the real key indoors and out of range.
the real, micro-chipped key must be detected, to prevent the anti theft lock-out.
most all similar starting issues i have seen were, coincidentally, on very cold mornings.
3. IF the above 2 do not help, again disconnect the battery, locate the fuse/relay block under the hood, unbolt, and make sure that all the wires underneath that connect to the fuse/relay sockets are not loose.
if so, push them all the way in/secure them, reattach the block, reconnect the battery, and, if necessary, relearn the key again
do not move on to #3 unless the first 2 procedures are less than successful.