No running lights on my trailer.

The trailer light are connected to you vehicles wiring. Turn brake running. If the tail light are on on your vehicle you start checking wiring. If the tail lamps do not work check fuses in vehicle. If the trailer is hooked up and the fuse blows again check trailer. If it blows agin without trailer check vehicle wiring.

If you have your owners manual it will be in there.

Headlights must be on for the interior trailer light to work.

does the 3rd brake light in the back window work? check fuses if fuses are OK and the hazard lights work, then the turn signal switch may be bad. I dont know what your sons suburban (trailer?)has to do with your navigator?

Check this location. They have color codes and wiring diagrams. Make sure the trailer has a good ground. It MUST have the ground wire connected to the truck and trailer or you will have a floating ground through the ball. That will cause blown fuses. http://www.etrailer.com/faq-wiring.aspx

Did you check the fuse for the trailer tow adapter paring lamps ? This is a separate fuse powered by a relay, it is not the same circuit as the truck's parking lamps.
This is fuse # F10 & The half size ISO relay, R201 in the fuse panel in the passenger side kick panel.
This is based upon being a new body style 2004, not the 2004 Heritage or Lightning models, those are different fuse & relay locations.

The description of the problem is very confusing. If the trailer is disconnected, do all of the functions work OK? If so the problem is with the trailer wires. If all worked before you replaced the light, then thats where the problem lies. The turn signal/brake lights are a seperate circuit than the running lights. The brown should be hot with running lights, and the yellow and green are the turn/brake signals. The trailer lights should be grounded to the trailer frame, and the frame connected to the white wire, Make sure the white wire is connected to the plug on the truck side and connected to the frame of the truck. The turn signal that works with only the running lights on doesnt make sense, and grounds are the most common item. Some Ford trucks have seperate fuses for right and left. There a small fuse box under the hood, near the brake booster.

I have a new F150 I have hooked up to my horse trailer. Running light work but when I turn on a turn signal this blows the fuse to my running lights, any ideas?

Also try http://www.etrailer.com/faq-wiring.aspx. They have a great website with lots of info.