I just helped my brother diagnose a no start on his Equinox. He had torn the dash apart to do the heater core. BTW EFFFFFF GM and the dumbass engineers that decided to design it that way.
Anyway, after assembly he tried to start and had radio, dash lights, etc, but no crank. He called me for help, because I seem to have to play hero anytime he gets into something. LOL He is in the car messing with it as I pull in the driveway and first thing I noticed was the reverse lights were on.
At first I dismissed it as courtesy lights. I tried a few tricks I have learned over the years and got nothing. Finally I decided to jump the starter relay. I touched it just enough to see if I got anything, and it cranked. I put the ignition into the run position, and had him sit in the drivers seat and hold the brake just in case.
I jumped it over again and it fired right up. That's when he realized even though the shifter said it was in park, it was in reverse. That explains the reverse lights I noticed.
After a little digging he realized that somehow the cable had popped off the shifter upon reassembly. He tore it back apart enough to pop it back on and after that he was able to start it with the key.
So, I've rambled on, but I was hoping to point some things out to you along the way.
#1 Try moving the shifter to neutral and see if it starts there.
If it does not then you can try #2 Remove the stater relay and use a piece of wire to jump across and see if it cranks. BE VERY CAREFUL if you do this. Have a second person in the car behind the wheel just in case it is in gear.
If it does start after trying that then you need to start diagnosing why it won't start like normal. I have had older vehicles that I sometimes had to "slam" into park, because I would have the same issue. Come out to leave and it won't start. It got to the point where I just pulled the shifter into neutral to start until I got the cable adjusted better.
Either way, good luck.