Blowing warm air inside,blowing cool air outside

could be a gas leak ( low gas pressure shut off switch, failed start run capacitor for the compressor , vermin problem shorting out the power board outside
The inside unit is just a fan
call an accredited ac technician to get a proper diagnosis and quote

shut it off 4 hours with both doors open, let it fully defrost, put your frozen stuff in a cooler, then re start it, the evaporator coils make be frozen up

I was leaning towards a bad contactor. Either sticking sometimes or not making good contact. I would inspect the contactor for pits or burn marks near the contacts. DO SO WITH POWER OFF of course...but, what's the reset button you are referring to?? I'm assuming this is a heat pump, please send model number!!

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First off, check power:disconnect box outside may have fuses,then check power at fuse box.If you have power(220 volts) then check for 24 volts at T-stat line.Also, make sure T-stat is set to A.C.With power on go outside and listen to condenser unit.If fan is rotating listen for humming .If it is not running, it could be a bad contactor or a bad or capacitor .If it is running check after 5+ minutes if warm air is coming out of the outside unit.Also, wash the condenser unit:start by spraying the hose about 45 degrees downward ,going side to side,and down on all sides.Do Not use High pressure hoses,it will bend coil fins.After it runs for about an hour,or so, go out and see if low pressure line(big one) is sweating and cool, and high pressure line (small line) is warm.

Cooling comes from what is done outside, if air handler is blowing and you are hearing a sound , may be in the duct work. If you feel warm air in cooling mode then the outside unit is the prob, need more info

probably a.c. was left with out a gas,and compressor will not start and there is no cooling.

With a heat pump system there are always going to be a back up heat strip inside the Air Handler.

If you detect a faint humming in the Condenser call your local service company and ask them to come and replace your capacitor in the condenser. The humming is from the contactor engaging but not being able to start the compressor due to not having the required Microfarads to start it.

Let me know if this helps

Sound like air flow problem to me, the inside and the outside. check the inside filter to see if it's clean and clean the outside condenser coils by washing it.

You need to look at the outside half. See if the compressor is overheating and shutting of to protect itself.