tick-tick-tick sound when starting

First off, my experience with cars is very limited, so please be as specific as you can.

I bought a used 91' Beretta a few months back and it's been working well, but right now I'm having some crappy trouble. I'll make a list of information that may be helpful.

1. throughout my use with it, I've noticed that the headlights often dim when I'm sitting idle at a red light (but they're fine when driving)

2. when I try and start the car all I hear is a tick tick tick tick tick sound and the dash lights blink with the ticking sound. Mind you, the ticking sound is very rapid.

3. the lights work, even though the car won't start

4. the battery was jumped and it sounds exactly the same

5. I've been having trouble getting the car to start from time to time, but before when I turned the ignition, it wouldn't make any sound, it just wouldn't start. So I would turn it and try again, and then usually by the 4th time (almost never got to that many times), it would work.

6. I filled up my coolant container and like a month (certainly no more than 1.5 months) (just when this probably occured), I realized it was about empty. I did fill it back up though, and still not working since I last checked.


I think that's about everything I can say that might help. I'm gonna go check on it one more time and see if I can figure out more precisely where the noise is coming from. If I come up with anymore information that would be helpful, I'll be sure and add it.

Thanks,
Zach


UPDATE:

I turned the ignition and left it there for about 2 seconds and noticed that the ticking rate went down and now it only does a single tick/click. The headlights worked BEFORE I did that, but I didn't check them afterwards (I know the inside lights work).

I need some help! Anybody! This is my car for transportation to work!