'94 Cavalier RS

Well hello everyone. Gotta problem with my car and not sure what to do, despite of the 9 people that have given me their opinions already. I have a 94 cavalier and the other night I was driving and all of a sudden my lights slowly started to get dimmer and dimmer with every 2 minutes or so. Then my radio started cutting out and my my car just died mid roll. At first when I explained this to 2 mechanics and about 7 friends they said yer alternator wasn't charging the battery, which makes sense. I know nothing about cars but I did understand that. So I took my alternator into Murrays Auto Parts and had it tested twice and taken to auto zone and tested twice. They both tested it twice and they both said that it passed. I had it tested 4 times and each time was good. Now when I start my car, it idles for a good few minutes and dies. If I turn on any kind of accesory, it starts to die almost instantly. Many people say ignition modulator and that my alternator is bad even though it was tested. I don't know, but would love more opinions please. And feel free to ask me anymore info if I haven't given enough. Thanx in advance!

Check Your Grounds!!!!!

Please realize I know nothing about cars and I have no idea what that means. Please specify with details that a retard would understand.

Please have your battery cables checked. Auto Zone can check your charging system (in your car). They will hook a device to your battery while it is running, this can reveal a lot. You may also check the connections at the battery. If they are not secure this could cause your problem. They will also check the battery which can short out internally. This car will stall if this happens. These problems can very hard to diagnoise. Good Luck.