1992 Cavalier 2.2 liter

Your "smoke" could be clouds of condensation when your compressor doesn't compress enough to keep the evaporator core in your car ice cold. Your accessories (lights, etc) will continue to power on with the key on because they don't require a lot of power to do so. But your engine will not start if the battery doesn't have enough power to make the starter turn the engine, and it needs a lot of power for that. Clean your battery terminals first. Try getting a boost from another car. Or get your battery charged and see if it holds a charge. If the problem comes back after that it could be your alternator so get that checked too. Last thing I can think of is that you might need to change your battery wiring or keyswitch. I have a 92 cavalier 3.1 and I've experienced dead battery symptoms before too.