Well, here I go. I am making a few assumptions here. The first is that with the headlights on, and you attempt starting the engine the lights do not go dim. I am also assuming that for every attempted start cycle (turn of the key), you get only one click (If either of these two point are not true, check the battery connections, visually inspect 100% of the battery ground and verify that battery voltage does not drop with attempted start). With this being said, the problem is most likely the start relay or the start solenoid.
Check the start relay. It is located on the passenger side of the engine compartment just aft of the battery. The thing you hear clicking. I check this at the starter. On the starter there is one wire, which snaps on, make sure it is connected, if it is remove it and check voltage at the wire while attempting to start the vehicle. If you get approx 12V. during the attempted start, the start relay is working as advertised. Reconnect the wire.
At this point it is most likely safe to assume that the start solenoid located on the starter is bad. You can check this. Pull of the red plastic cap and you will see two nuts holding down two cables. The voltage at the long cable should be battery voltage at all times, it runs straight from the battery, let me say this again it is HOT! Try not to arc weld anything. Now check the voltage at the short cable that disappears into the starter. You should have 0 volts, becoming 12+ volts during a start attempt. This tells me that your solenoid is O.K and the problem is within the start motor itself. If you don't see 12+ volts during the start attempt, you have a high resistive load across the start solenoid caused from years of contact erosion. Last time I checked, you can replace only the start solenoid for about $40, the start relay for only $9. To replace the entire starter can cost between $129-160. So, if you troubleshoot everything you can save yourself a lot of money. I would like to stress one more time the need to check the battery ground wire they corrode all the time.
Good luck, let me know how it turns out.