i have a window unit fridgidaire model FAS257Q2A4 i can set it on energy saver & it comes on & goes off after a while but the compressor never comes on or cools
Is the outdoor fan running? Does the outdoor fan turn off when the unit should still be running in cool mode? Compressor may have a run capacitor or potential relay in it. Remove the cover from compressor and inspect relay. If compressor feels hot to touch after you had system running it may be off on internal overload due to faulty capacitor or relay.
I guess there should be issue with the outdoor fans, check if they are running?