I am in the same boat right now! My pickup coil went bad on me. The symptoms are simply this.
-It cranks but it just would not want to start
-There are time it does start and other when it dies.
-When it does fire up, idle is normal.
-If you never have changed the distributor and your car has high miles, then its probably time to change the pickup coil.
-In order to do this you WILL need to take out the distributor. Either to change the pickup coil or the entire distributor.
Personally, I would just change the entire distributor since you filled it up with antifreeze. The cost is just $30-40 bucks more but its worth it. Much easier to replace the distributor as opposed to changing out the pick up coil. You may need a professional try to help you change out the distributor because you WILL need to check the timing on it. If you don't have a timing light, or the right tools...you may end up messing up your car. Unless you are willing to spend more time reading up on how you can change the distributor and timing it...I would suggest to just purchase the distributor and have it changed. However.....
Make sure you have checked the following.
-turn the key ignition on and listen to your fuel pump...do you hear it come on? If you do then your fuel pump is fine. If you don't or hear it louder than usual then it may be your fuel pump.
-It could be your fuel filter....those need to be changed every 3rd or 4th oil change.
-If its not either of those two, check the spark on the spark plug wires. Turn on the car and see if you notice a spark. If you don't then you know you have an ignition problem.
-Check the ignition coil (the square looking thing that one spark plug wire goes to from the distributor cap) and take it to an auto zone for them to check it.
-If its not the ignition coil then that is when you check for the pick up coil within the distributor. My mechanic has seen many of these go out and are more likely to go out than the ignition coil. Hope this helps.
BY THE WAY, IF ANYONE KNOWS HOW TO SWAP OUT A DISTRIBUTOR AND TIME IT CORRECTLY PLEASE LET ME KNOW. I APPRECIATE ANY INPUT. THANK YOU. (ITS FOR A 95 GT MUSTANG)