Car Not Starting

I do have a question regarding my car not starting. I had pulled into a store parking lot and shut the car off and when I came back out it would not start! No sound as if it was trying to crank over, nothing. I thought I could hear a faint clicking sound coming from near the fuse block under the dash on the driver's side, but I am not one hundred percent sure. Everything else seems to come on, the headlights are bright, the radio comes on, as well as the blower motor, wipers, dash lights, etc. I put new battery terminal connections on, and I had even gotten a jump from a guy at the store and it still would not make any sound as if it was trying to turn over. With the starter being in such a difficult place to either check or remove and check, I have not done that yet. Is there a way to check the starter without crawling under the car and if it is not the starter, what would your best guess be as to the cause of it not starting? It seems funny that when I started the car to go to the store it started fine, but ten minutes later nothing? The car has never given any indication of the starter getting ready to fail altogether. Thanks!