Welcome to Bonneville Club, Pat. Please put the year and model of your car in your signature. (Edit your profile to do this.)
You need to peel back the covers on the ends of the battery cables and examine the copper conductor and the crimps for corrosion. If you cannot make it nice and clean, you will need to replace the cables. And, you need to do the other ends of the cables where they attach to the starter, the alternator, the engine block and the engine relay center on the firewall. The grounds should also be clean and bright, coated with dielectric grease and re-tightened. Make sure you do the body ground from the negative battery cable, the group of grounds under the ICM, and the PCM ground near the oil filter.
Also, check the ground buses under the kick plates inside the front doors.
If that doesn't help, and you know the battery is OK, you may need a new starter. But, even a new starter won't work with poor connections. You may want to put a test light on the solenoid lead to make sure you are getting 12v at the solenoid when you turn the key to the start position. Finally, make sure the starter bolts are tight and that corrosion has not blocked the flow of current from the engine block to the starter frame.