The fridge and freezer will not get cold, the fan is running

for the noise check the compressor groumits

FRIDGE COILS or door walls SEEM VERY HOT:

The condenser coils do get hot. They can even be to hot to comfortably touch and this is normal.

The refrigerator should not run constantly but shut off with each defrost cycle.

Running constantly and never cycling off can indicate a cooling problem.

One thing to try is to wait till it has been running a few minutes then open the door and turn your cycling thermostat towards the off position. It should cycle off before getting to the off position on the dial.

If it does not cycle off then it's not getting cold enough to satisfy the thermostat. This is likely the reason the refrigerator runs all the time.

A thermometer in a glass of water can be used to check the temperatures in the refrigerator section.

You can check that all fans are running.

the reason the outer side of the door seal area is getting hot is the compressor is over heating, probably the condenser fan motor to your compressor is bad.
It should be a little warm but not hot. they don't use heaters anymore ( some older models still use heaters) around the doors, instead they use the condenser coils to remove condensation and moister, you might want to check your condenser coils on the bottom or back of fridge to see if they need cleaning
If the condenser coils/condenser fan are all plugged up they need cleaning and/or the condenser may fail or has failed..

The ones that use an electric heater will have an "energy saver" switch that will turn it off.: God is the reason I give you free advice so God is good!

FRIDGE COILS or door walls SEEM VERY HOT:

The condenser coils do get hot. They can even be to hot to comfortably touch and this is normal.

The refrigerator should not run constantly but shut off with each defrost cycle.

Running constantly and never cycling off can indicate a cooling problem.

One thing to try is to wait till it has been running a few minutes then open the door and turn your cycling thermostat towards the off position. It should cycle off before getting to the off position on the dial.

If it does not cycle off then it's not getting cold enough to satisfy the thermostat. This is likely the reason the refrigerator runs all the time.

A thermometer in a glass of water can be used to check the temperatures in the refrigerator section.

You can check that all fans are running.

the reason the outer side of the door seal area is getting hot is the compressor is over heating, probably the condenser fan motor to your compressor is bad.
It should be a little warm but not hot. they don't use heaters anymore ( some older models still use heaters) around the doors, instead they use the condenser coils to remove condensation and moister, you might want to check your condenser coils on the bottom or back of fridge to see if they need cleaning
If the condenser coils/condenser fan are all plugged up they need cleaning and/or the condenser may fail or has failed..

The ones that use an electric heater will have an "energy saver" switch that will turn it off.: God is the reason I give you free advice so God is good!

Try the self help section of repairclinic.com. You can get model specific trouble shooting advice there.

Is the cooling fan for the compressor working? There is a coil of the condenser line that runs around the freezer side. This will get hot but the cold freezer side keeps it form not getting too hot. It could get very warm if the freezer is not cold yet.

ok well... those pipes coming from your compressor one of them should be hot. if not your compressor is not running.

It sounds like your compressor is going bad. The part you mentioned being hot is normal.

Replace the start relay on the compressor.

there is another fan at the bottom, rear, of the refigerator. remove the bootom panel and look at the cooling fins to make sure they are not bent into the fan blades. Caefully bend the fins away from the fan. this should improve the cooling of the refrigerator and get rid of the hot spot on the rail between the refrigerator and freezer.

"Fan in freezer does not seem to be running"

This wiil cause it to frost up in the freezer and this fan is the only way to get cold air into the Fridge area.

If you remove the back panel on the inside of the cabinet then you would be able to check the evaporator coil (cold bit) and see if it is frozen up. If it is then defrost the system and see if you have any improvement. All the things you have pointed out over the compressor is normal, they do run incredibly hot. If you have got the freezer on a very cold setting I would suggest bringing both setpoints to a mid range setting. Check the temp in the fridge by measuring liquid temp as air temp is prone to fluctuate more. If you still have a concern I would suggest contacting a fridge guy to assist you. Hope this is of some if not limited help.