Electrical testing and troubleshooting
The problem you have requires some patience and systematic searching for the problem. I would get both the circuit tester described above, and an inexpensive multimeter (about $15 at Radio Shack). The multimeter can be used to measure a variety of voltages, both AC, such as shore power, and DC, such as your battery (DC voltage gives you a reading on the charge state of the battery, plus resistance, good for checking fuses and circuits for good connections.
In your case, I would start at the source for the power, and work 'downstream' to the individual circuits and components on those circuits. don't forget, your furnace changed or was worked on (blower, 12 volt). For example, do I have 120 volt at the plug for the trailer? Then, do I have 120 volts at the trailer receptacles? If not check for tripped or bad circuit breakers... Is the Univolt o.k.? You can check for a bad circuit by, in the extreme, removing all fuses, testing them, and adding them back one at a time.
You can do an Internet search on testing fuses,and circuits, and troubleshooting that should help.
Sorry to be so long winded, it's a little hard to gauge from text messages what your level of expertise is.