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What system do you have, dual or manual? Has the AC been working or did you just get this car? Give a little more background and I am sure you will get some useful info. Have you put any dye in the system when you recharged it? That would probably help. Usually if the light goes right back off , its a sign of low freon. How are you checking the freon level?
R134 is not the same as R12 in the old days. You can't just add refrigerant on a whim. The system pressure is based on the volume for that system, ambient temperature and whatever else needed. The best advice I have for you is to take it to a professional shop where they'll evacuate it and recharge it with the proper amount. Too much or too little refrigerant will cause it to not work.
I had a similar problem with my 01 a few months ago. The compressor clutch would not engage. If I pushed the AC button, the light would go out immediately. I had a mechanic friend check the freon level and he stated it was full. He disconnected my battery for a few minutes to see if it would reset - Nothing.
I was getting ready to take it to a specialized shop, but decided to try out some advice that was given in a post, which was to completely disconnect the battery for like 10 to 15 minutes. Guess what, IT WORKED. I guess my friend didn't disconnect the battery long enough. Also make sure your battery is fully charged.
I know in your first post you stated that you added freon. It's possible that now your system is over serviced, but next time the compressor doesn't engage, try disconnecting the battery for sometime before doing anything else and make sure your battery is fully charged.