Weird!!! When engine light is turned off - AC starts working

My engine lights comes on - reads closed trottle position - AC works only when going over approx 25 mph.
Auto zone turned the engine light off and AC works perfectly. After about 100 miles, the engine light comes back on and the AC begins to work only when driving over 25 mph again.
I have had Auto zone turn off the engine light 3 times now and the AC works again each time.
Has anyone out there had this problem? I guess the best thing for me to do is buy a scanner to turn the engine light off myself.
Any suggestions out there? Thanks

My first guess is that your car is going into "limp home mode" which it will do when it detects a serious problem. First check the condition of the fuses on top of the battery. Do you have any other symptoms?

I appreciate you responding to my post. The fuses on top of the battery look fine, but maybe I should change them out anyway? The only other problem is that it does seem to hesitate between 1st and 2nd gear, but not bad. I've cleaned the MAF with CRC, but maybe I should have a tune-up. Changing the plugs looks like a chore, but this 2000 beetle has 174,000 miles on it.
I've only had it for 2000 miles. It probably hasn't had a tune-up in a while. Can regular auto repair shops like Precision Tune or Pep Boys
tune these new beetles up or do you have to take it to a VW dealer?
Thanks for your reply.

First I'd change the plugs which are difficut but not impossible and also put new leads on at the same time as they can cause a stumble if dodgy. I'm in Australia so cannot comment on Autozone etc but from what I've read you need a Vac-Com or similar device OR go to VW for a full scan of logged faults. At your mileage you may have heaps of logged faults!.. Tuneups - nothing to tune in a modern car! - just replace components.
Also throw a tin of injector cleaner in the fuel tank - it may help. Good Luck.

Thanks Hako for your help. I hope that since I bought this car at a good price, because of so many miles, that the prior owner took care of most of the problems.
I will change the plugs & wires and look into getting a scanner off e-bay. Thanks again for your help.