It is either a bad relay-overload or a bad compressor, if there is a capacitor on this freezer it is a run capacitor and it would still run.

Take the relay off the compressor and take them to an appliance parts store and buy a replacement and see if it works OR call a repair person and get them to check it out.

You are correct that it is usually too costly to replace a bad compressor and not worth it on a plain freezer.

John L.

If you can get a new relay, it will not match perfectly to the current one and very likely won't mount the same way.  You might just need to tuck it somewhere secure instead.  So if you need to compromise the mounting system on the current relay in order to get it out of there, it won't likely matter.

I would try not to disturb the compressor on a system as old as that one. 

Yay you got it off, A new relay will plug on the same way but it may look different.

I think you still need a new relay, the burned wire would not cause the problem you were having.

Your old relay was sticking and by removing it it unstuck, you can try soaking it with a silicone lubricant etc which might keep it going but it would be better to replace it as it will probably stick again when you have the freezer full of food.

John L.