if the cables are tightly attached to the terminals then that shouldnt be the problem, sometimes the lights and accs. will work on my car but when i try to start it it clicks loudly and all i have to do is tighten down the battery cable clamps. -

 

It sound like you have what is known as a flat spot on the starter. to test this the next time it does it tap the starter with a hammer if it startes replace the starter.It would help if you have some one to hold the key on as you tap it but make sure you are not anywhere near the fan or anything else that will move.