My kenmore 19.7 cu.ft. chest freezer is not running and the compressor is hot

If, by plug in you mean the socket, then you need to check the fuse in the power plug next.
At the very lease there should be some light on the unit that illuminate even if it does not FREEZE.
If the compressor comes on wait to see if there is any drop in temperature. then it is possible the fuse was faulty.

see below links for more information on possible causes




How to fix Kenmore chest freezer model 255 19502010




Kenmore 5 cu ft 142 liter Chest Freezer 14512 Page 11 Recent Questions...

It looks like a bad ignition switch or capacitor. This is not that expensive. Probably not the compressor. Unfortunately, one small part stops the whole show.have a friend who is a tech look at it.

check seals around door make sure there no leaks,

Possibly. However it sounds like the compressor is running hot which could be the relay assembly sticking with the start windings in the circuit.
Eric

. Cut everything off for a few minutes then turn it back on and listen for a click from the compressor relay as the compressor tries to start.
Is the compressor motor running.If no check starter/overload relay.
http://www.acmehowto.com/howto/appliance/refrigerator/refrigerator.php

u either need a new thermostat or your compressor is dead

Believe it or not, but it is normal. Especially when just turned on. As the internal temp. gets colder so will the temp. on the side get cooler.

Make sure you have power going to the unit. Check the thermostat for power on both sides going in and coming out. You need to give me more info. before I can suggest anything else.

Remove the back panel, if there is one, find the compressor. Put your hand on it. If its very hot, you have a problem. You should feel a slight vibration if good and running. If The overload is shutting off keep your hand there and wait a few minutes, see if there is a clicking noise coming from the compressor. This is just a start, but you said it has been off for a while so my first suspect is a compressor. Do these things and let me know for a follow up.