1995 cavalier

Put that $1.98 continuity checker down for a second and check for voltage with something starting from the battery. What work has been done recently? That's often a big clue. You didn't just change the starter did you?

Then go to a professional mechanic and pay for professional adivce...

I had a battery in a car that would report 13V on a multimeter when there was no load, and reported fully charged from a battery charger. Turn on the headlights or starter, and the voltage would go down to 0V. The battery was shot and had to be replaced. It suddenly failed with no previous indication that the battery was on the way out.

I would check the connections on the battery too. If they are corroded, try cleaning them off, reconnecting the cables, and securing tightly.

As a PROFESSIONAL mechanic I cannot help you without prior payment so send a check and I will then tell you what the problem is.