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Sounds like it may be low on Freon. Does the blower still work on heat?
Yes, start here. But first, undo the negative cable on the battery for a few minutes as that resets the system.
If you restart the car and everything work then stops you will probably be low on Freon. If you then check the diagnostics you will probably get an "09" error code which means low Freon.
If you Freon is good check your cycling switch as that could have gone bad with time. They are about $15 at the parts store and take 6-7 minutes to swap.