8" burner isn't working. I  am getting current at the electric receptacle.  8" surface unit is beat up.  looks like shit..  

If you have a multimeter you can test for a resistance value on the heating element and then check for a short to the out metal casing.





If you don't have a meter (and don't want to spend ~20), the elements are cheap; just replace it and see if that fixes it.

How many 8" burners do you have?  Can you swap it with another one?  Might be time to replace it.

Check continuity on burner element and replace if it fails.  Burner elements are fairly cheap.

It could also be the socket the coil plugs into.  I've had to replace coils & sockets several times on our Kenmore stove, mainly because we (ab)use it for canning and may have several big pots on it at a time. The big pots overhanging the coils reflect heat back down into areas where it doesn't belong, frying the sockets and wires.

ETA: just noticed OP said there is power at the electric receptacle...(coil socket?).  If so that's obviously not the problem.

Only got 1 8" on there.  Gonna order another off the web.

Order a socket while you're at it.  They are cheap but easy to replace.