The first thing to do is locate the break in the wire, using a wire break locater. Another option is buying a device from Petsafe which allows you to use an AM radio to find the break. Once you find the break in the wire, repair it according to a wire repair guide.
Because the wiring is basic copper, use a standard wire connector if the system has been severed. If the green light is on the system is still working. Hopefully this is the answer you were looking for.
If your invisible fence is not working there is probably a break in the wire that forms the barrier. You must first locate the break. Next you will need to reconnect the wires by crimping them together. You might find it helpful to consult your fences user manual or the manufacturers website for more information.