Actually, "turns over but won't start" is actually kind of rare. "Won't turn over, won't do nothin' " is common and is almost always the damn RCM.
You might read the codes since you say the CEL is on, but frankly, I think the CEL comes on during all starts. There may be no codes.

So, first thing: Get in car, turn key to ON and listen carefully - do you hear the fuel pump run for a few seconds? It should always run for a few seconds, then if the car is not started, it cuts out.
If it were me, I'd first verify I have spark when the engine turns over (if not, check fuse 11, suspect maybe a bad Crank Position sensor,) then measure fuel pressure at the fitting on the end of the fuse rail. 55-58psi is specification. You need fuel and spark to start the car - so make sure you have both of them.

The way I check for spark is to just go buy some random spark plug, pull a plug cable off one of the plugs, and plug the spark plug you bought into it. Ground the body of the plug, get someone to hit the key, and verify you see a spark. If you have spark and fuel pressure, I'd wonder if the injectors are firing.

And if you have no spark, the crank sensor would be suspect, mostly cause crank sensors tend to fail - but most of the time, they fail at high temperature and if you let the car cool off, they start working again.