It has the original battery and has always started immediately.

If battery and connections are good-check the start fuse 5amp, park and neutral position switch, starter relay and starter itself-

I would definately suspect the starter solenoid. An easy shade tree way to check that is have a buddy turn the key over and hit the starter with a hammer. If after a couple of solid hits the car starts then you need a new starter. While under there check the electrical connections and see if you can wiggle the starter at all. Sometimes the starter will get missalligned and need to be re-tightened or shimmed.