My Parmak solar fence charge does not work. I have new battery. I opened the metal box with all the capacitors and wires and there is a yellow wire that came unsoldered leading from the little electrical displayed gauge mounted on the front of the metal box. Where does the yellow wire go?

The voltage out to the fence is too high for a regular multimeter to read.
See if this general application video helps.
9 Troubleshooting your Electric Fence

The click is the transformer carrying current. If the unit doesn't click, unhook the fence from it and turn it on. If it starts clicking it is a short on the fence. If it doesn't then the unit is not working. contact parmak and they can service it or sell you a replacement circuit board which is the most common failure.

I would first start with the battewry, 2 year run on battery is pretty good. You can go online and find replacement batteries or go to place of purchase and check with them.

if the unit is not produceing a charge during daylight then it is the unit. the DF-SP-LI will produce full power under sunlight alone. test the unit with the fence unhooked.

disconnect the unit from the fence and turn it on. if the fencer work(ticks, meter moves) then it is a fence issue(short, broken wire). if it doesn't then it is an issue with the unit its self and it will probley need a PCB or service.

With the fence connected or not?. with; then disconnect and turn it on again . if it works fence problem if not unit problem. with-out; unit problem . most likely PCB

solar panel went kaputs they dont last fore ever go to radio shack they have solar panels

If the light stays on stead then that is a PCB failure, specifically the SCR is "motor-boating" .

I have see this happen before and its usually do to most moisture/rain getting in. ie use multi meter to varify solar charger putting out current/voltage. Odds are its not anymore. Rechargable batteries are notorius for not lasting but not in 2 months.

I WOULD THINK SO BUT THE BLACK MAT BE THE POS. AND YOU MAY BURN UP THE CHARGER IF HOOKED UP WRONG BUT OTHER THEN THAT YOU HAVE GOT I THINK