can you take another pic, indicating which way is up?
On top of the drum containing the motor and compressor, there is usually a plastic dish to catch the condensate, and the heat from the motor evaporates it. Does it have water in it (it may be very dirty. You can sponge it out with detergent, after unplugging the appliance. Do not allow water to drip on any electrical part).
the brown/black stain might be from the grimy water in the condensate dish or tube. If so, it may clean off if you sponge it with detergent (after making sure it is unplugged)
try to take a close-up of the brown mark. Sometimes rodents gnaw plastic parts, including cable insulation (so unplug it first)
give the motor/compressor cylinder a wobble. It should be bolted down on rubber feet that absorb vibrations. These might be worn, loose or perished (they can be replaced)
if the cylinder feels very hot, the compressor may be struggling. This could be if it is short of refrigerant gas, or it could be that the internal cold air channels are blocked with ice (this is common in "frost-free" freezers, but they can be manually defrosted. It is very slow).
Also, clean all the dust off the coils on the back with a soft brush and vacuum cleaner hose.
Check that the back and underneath are clean and dry before you plug it back in.