Intermittent starting problem

I have an 89 camry with 185K miles and have recently experienced the following problem. When turning the key to start, nothing happens. All ignition and dash lights illuminate normally but the starter will not turn. I cleaned all the starter and battery connections, and went as far as cleaning the rotary ignition contacts in the steering colum. This problem occurs intermitttently, when car is hot and cold. When it does crank, it turns over strong and starts right up. I suspect a starter relay but I'm not sure where its located. My local tech thinks it might be the starter and that the relay is located in/on the starter? Any suggestions??

alot of times its the starter contacts....next time the starter acts up try lightly tapping the starter with a hammer and see if it starter up...