OK, so you're engine won't turn over right? It just clicks. This is a sign of low or no power getting to the starter. The usual cause is bad/dirty battery cables or connections. My first GUESS would be at the starter. I'd clean them all to be sure. Both at the battery and the starter.
********I have a '94 grand prix that just started doing something similar. Most likely a battery/power issue, what you need to do is have someone check and see (when the car is started) if the battery is getting charged by the alternator. (of course after you check battery terminals for corrosion because a bad connection could explain why it sometimes starts and sometimes doesn't) If the terminals are clean there probably is an issue with the battery not charging causing the clicking sound usually caused by low/no power from the battery, also try checking if the battery is bad... might be time for a new battery because it might not be holding a charge all together.******
I have heard the alternator does it,cold drains the battery too,if it's not started for awhile can kill it.
Check the battery mine 1995 Z71 did the same thing changed starter still did same thing finally was told to check the battery after it sets awhile battery does not have enough juice too kick the starter in I had battery checked sure enough on cell on battery was dead bought new one not a problem since.
I've come to the conclusion that the starter gets too hot.. try getting a gel battery they have true cranking amps alot better
Most likely the starter should be replaced. When it heats up, it will turn the engine with a lot of strain. like the battery is low. When it cools down, it will turn freely.
Is it a problem of the battery goes dead or does it crank but not catch? If the battery is going dead over time perhaps you need to check the battery and/or alternator. If it's cranking but not starting, check the computer codes.
Any time you have no power to the headlamps I would concentrate on a bad battery cable or ground cable or battery connection. It works now once in a while, but if you don't get it taken care of, it will soon fail totally. Trace and clean all connections starting from the battery back thru all connections and DON'T skip any that "look good".
You should take the battery out and let it sit for awhile.
Probably a bad spot on the stater or the solenid
could be a weak battery, not turning engine fast enough at startup. check battery voltage should be approx. 12.5 volts when not running.about 14.0 when running.
"hot start" issue. Could be the solenoid, or starter itself.
there are nine members last time i checked. if there are more now that's becuz i checked awhile ago. hope i helped though :)