[erps]

The click you heard was the starter solenoid switch closing. Two things are possible. Either the engine was so hot that it was partially seized, and the starter couldn't budge it or the hot starter had high resistance and couldn't pass enough current through the contacts to spin the motor. I think the second was more likely.

Were there any other problems with the cooling system that may have caused the over heat problem? An overheat due to low oil is quite a bit more serious than a overheat due to low water.