When Rich mentioned a "tester", he was talking about something like this, shown in a utube from etrailer:
I have one of these also. It's a VERY simple way to find out if things are good at the Tow Vehicle end. A common problem is that the trailer battery charging fuse in the TV will blow. This device will tell you if that has happened. You can order this tester from etrailer or other sources, such as Amazon ($8.92 right now).
Then, if your TV output is good, it's fairly simple to check the trailer, because you just have to follow the brake wiring from the plug back to the trailer brakes. You will be looking for breaks in this circuit, especially where it is attached to connectors. My brake wires were connected to the feed line (near the axle) with wire nuts, which I don't think is the best way to make connections that are subject to environmental abuse. I replaced those connectors with ones that were weatherproof.
You should see a ground wire from the brakes too, probably white in color. Make sure it is connected securely at both ends.