The problem you are having with the AC digits blinking is usually caused when battery is disconnected with the air conditioner operational. The air mixture door gets out of sync with the computer. The fix involves removing the glove box and resetting the position of the door. If you search the forum you should find a detailed explanation about how to fix it. Of course, getting the glove box out may seem daunting at this stage, but it's really quite simple.
There are some active threads about PA's that won't start or die while running and much of what you need to do is covered in them. This can be a long process of trial and error. So be patient. Help is on the way.
Searching through this forum is a great place to start on your repair...take some time and read over what others have experienced. As you probably know, it just about has to boil down to fuel-air-spark-timing. There may be some codes stored that can point you in the right direction. There's a way to do this using a paper clip and is documented here in the forums and probably all over the Internet.
Checking for codes is probably the best way to start. Please post what you find out. Sorry, I got to go eat dinner.
Good Luck!