93' Lincoln town-car needs help of diagnosis of what is wrong with it?

How do I figure out what could possibly be wrong with my car? My car is a 93 lincoln towncar that would run perfectly fine and just recently stopped working. Now it shows lights when trying to turn it on but does NOT start! Who could I call to give it a good look and get worked on. Also what can i do to try to figure out what could be wrong with it.

I was told that it could possible be the alternator or the battery but they was not for sure if that could be it though. Could my engine have locked up if I didnt let it start and run for a minute before driving it. It has always been a problem to let it run for five minutes or ten when i have driven it at all and it would not pick up and go when i did leave before it had a chance to run. Could that be the reason why its not working no more?? Again the lights come on the car just wont turn over and it clicks when i try but shortly after the lights go off when i try.