Z -
With shotgun replacement of parts, I think you are headed for a dead end, and an expensive one. Take a look at this article on the e-trailer.com web site.
http://www.etrailer.com/question-70204.html
On the Prodigy P2, the OL indication means "Overload". No surprise here. It can mean that you have a short circuit somewhere in the brake line, and the short is demanding too much current, which overloads the controller. You would think that this would blow a fuse, but apparently that isn't always so. However, I consider this an unlikely problem.
The surprise (to me, anyway) is in the fact that the OL indication can also mean a poor (but not completely open) ground connection. This is much more likely - read MUCH more likely. A poor ground can show up in any number of places in the brake circuit.
The first, and easiest, place to check is in the Bargman connector, where the TM plugs into the tow vehicle. Open up the little door on the rear of the car half of the connector, and peer inside with a flashlight. If you see any corrosion anywhere, get rid of it. An old toothbrush is a great tool for scrubbing around in there, and a bit of baking soda on the brush will help. When done, clean out the connector with a good spray of water, prop open the door, and let it dry thoroughly.
While it is drying, look at the trailer half of the connector. This is a bit harder to see into, but you still might see some corrosion. Whether you do or don't, it is still worthwhile to cut off a narrow strip of a 3x5 index card or the like, double it up until it is thick enough to drag a bit when you push it into the slots, and scrub it in and out of the slots. If you have an auto supply store or a Radio Shack near you, get a can of contact cleaner, and spray it into the slots while you do it.
The next step is to check the connections under the TM, just inboard of each wheel. As I recall, there are two wires that come from the front of the trailer to the street side wheel. At that point, each wire branches two ways - one way goes to the brake on the street side, and the other crosses over to the curb side wheel. These connections are made with wire nuts, and corrosion inside the wire nut is common. Check the connections on both sides of the trailer. If you find anything bad, clean up the connection and replace the wire nut with a new one. I recommend the blue grease-filled wire nuts as replacements.
Almost every brake-related bad ground will be found and fixed with one of these steps.
Let us know what turns up.
[RVCycleGuy was typing while I was. I should type faster! Or shorter ...]
Bill