Are the lights bright but dim slightly when you turn the ignition key to "start"? Try "jump starting" your car off another car just to help eliminate the battery as being the problem (allow the other car to run for a few minutes and make sure your connections are good). It is likely the starter solenoid on the starter has failed. But I would check for power at the starter when key is in the start position (power should be present on the smaller wire at the starter when the ignition key is in the cranking position only) and check battery power and ground cables are clean (free from corrosion) tight and secure.
Starter is not easy to replace in that car, intake manifold needs to be removed.
Thank you Patrick! The lights did not dim. The next morning, I tried to start the car and it made the
"dead battery" sound- click, click, click. So we jumped it, drove it to Sears and they checked for output.
The battery checked out. New cranking power is 880 amps, it checked out at 760. So, that little dome light drained the battery in just 2 hours! I should say the battery is a Sears Platinum and is 4 years old.
Thanks again, Merry Christmas!