One of my kids cars died on him a couple nights ago and had same issue.
Lights, windows, etc worked fine. Had the battery checked (took 58 minutes) and it proved good.
Pulled and had alt tested and it failed almost immediately.
So... with that in mind. The fact the lights, power windows, etc worked means the massive batteries in these cars may have signs of power but not enough amps to turn the starter. If you want to see if alt is good, after you push start the car check the volts at the battery when running. It should read 13.4+ volts.
1) pull battery and take to Autozone, AdvanceAuto, Pep Boys, etc and have them test the battery. If it passes, read on. (10mm and 13mm wrench)
2) check the cables at battery and at the alt/starter paying special attention to ground cables.
3) pull the alternator and have it checked at Autozone, AdvanceAuto, Pep Boys, etc. (std screwdriver, 10mm, 13mm(x2) and 19mm wrench.)