1991 Pontiac GTA, starter?

I have a 1991 pontiac gta, it has about 101,000 miles and is due for a tune up, I have been having some issues with it starting for a couple weeks now somtimes it would start right up and other times I would have to try turning the key a couple times before it would turn over at all, the other day I went out to start it and nothing happend I brought the battery in today too see if it was good and it was not, so I bought a new one threw it in and all my electrics work I turn the key and hear the fuel pump turning on but the darn thing does not turn over, nothing happens I cant hear the starter clicking at all I was wondering if I should replace it? Or if I could rebuild it I am a mechanic just not a car mechanic I work on helicopters its a big difference haha