Key will not turn on anything intermittently, but then 15 minutes later, will work normally

Could be a bad battery or your battery cables could be loose or corroded so there is little power getting to the starter.Check all battery cables at both ends and might even have to take the cables off the battery and clean the connections hook up to the battery.

Having to let it set for the 15-60 minutes, sounds like theres an electronic component, that when it gets hot it looses contact, or the component is bad and when it gets heated up, it goes out, and when its allowed to cool, it starts working again, have the wiring harness checked where the harness plugs (3 plugs) connect to the ECM. Hope this helps.

could be the security system. is the key an original or one made later? the keys have a chip that must be programmed to the particular vehicle. try turning the key to on wait i think 15 minutes the turn the key off then try to start.

get it properly diagnosed at a reputable repair shop. does the dash stay lit when ur cranking?(turning the key all the way trying to start it) does the security light stay on or flash? im thinking a security problem. its not reading the key right possibly. not uncommon now for this to happen to newer cars.

to reset theft system--turn key to on, leave for about 15 minutes. after 15 min. turn key off, wait 15 seconds. then try to start car. to bypass anti theft system-- all gms===go to site- newrockies.ca/vatsbypass.

could be the starter but could also be a relay that is not working properly. the relays are under the hood. you would have to have someone under the hood and someone turning the key at the same time to see if the relay is working. if it works every time you turn the key then its probably the starter.

sound like leaking fuel injectors.have them cleaned and check.they are flooding out engine.when you turn off engine.they will continue to drip.

P1361 TDC Sensor Intermittent Interruption (I got this from Engine-Light-Help.com)
TDC should mean Top Dead Center.
It is the sensor that tells the computer the #1 cylinder piston is at the very top. And therefore, fires the spark plug.

Since the maintenance done above, I believe the the timing marks for the timing belt is not lined up properly. Being off by one tooth will cause this problem.

I had the same problem only a few months after I bought the car new in 2003. Dealer fixed it. Then 6 months later same deal. Finally I went to a 3rd party and ordered new different brand remotes and figured out the programming which was quite simple. A serirs of procedures with the door and the key which programmed the devices. 5 years later no problems. Of course before you do anything try replacing the battery in the remote.

Be sure its all the way in park or try neutral.Its possible that security system does not recognize the key. Is security light flashing or on steady? Shut all doors and windows,trunk,hood, turn off all accessory's,roll down drivers window, turn key off and remove for at least 1 minute, insert key into ignition, try to start leaving key to run position for 20 minutes, turn key to off,wait 15 seconds, try to start again leaving key to run, wait 20 minutes, turn key off,wait 15 seconds, try to start, again leaving key to run, wait 20 minutes, turn key off, wait 15 seconds, try to start. This should relearn key code. It may relearn after 1 learn cycle and start if system is ok. Hope this helps and that the weather is dry and warm for this procedure! This is not always a fix, but works most of the time.