Crazy starting issue please read .. pulling hairs already can't figure it out
 

working on my daily driven Cadillac STS.. have a read and you'll be puzzled to .. any advice would be greatly appreciated I have been running around trying to figure this out for the passed 2 days .. Ok.. here it goes. 2005 Cadillac STS with the 3.6 engine. Car does not start. I push the start button and the dash goes black but no start. Then 30 seconds later dash comes back on. Here's where it gets tricky... i have replaced the starter relay and stil nothing .. but if I jumper the starter relay with a paper clip ... the car will atart and stop as it is suppose to with the push button.. but after sitting for more than an hour or so it goes back to being stubborn... and I cannot start it with the key unless I jump the relay again.. I have been running circles with this thing for the passed 2 days to try to figure it out. From my tests .. battery is good . Alternator is good. Starter is good since it will start the car when relay is jumped. Let Me know if you have any suggestions. My next bet is the ecm ..