The first place I look on the trailer is the master cylinder. Pull the plug and look for fluid. The reservoir should be full of clear brake fluid. If it's empty or full of water or rusted fluid you'll know it isn't right to start with. An empty reservoir means a seal is bad somewhere or a brake line is damaged or rusted through. Rust typically means that water has entered the system either through the brake cylinders or master cylinder. The master cylinder is usually more expensive to replace but any rust is bad as the entire brake system at a minimum will need to be flushed and the entry point of the water will need to be found.
I looked at two boats for my brother in law last year. Both sellers had told us that the trailers were in excellent condition and that the brakes were in good shape. One had no fluid at all in the master cylinder and the other had rusted fluid that looked more like water than brake fluid. After showing this to the sellers they still insisted that there was nothing wrong. We walked on both. Figured if they were that clueless on this how were they on any other aspect of their boat. One of those boats is still for sale on Craig's list.