I don't know about the DG1 head, but as a rule with my experience I would smell the unit for any obvious smoke damage, like shorts, then look for any fuses, they sometimes have black caps on the outside.
I would inspect the wiring for damage then plug it in and check the voltage in the bulb socket. Check the bulb. Then if nothing, open the case and look for shorts and inspect the wires to make sure they are hooked, soldered, in ok. Check the transformer, input and output, with a multimeter. You can get one cheap at RadioShack etc.. If it's not the wiring, fuses, transformer, bulb socket then it's the electronics in the circuit boards or if they are removable clean them. The Beseler heads I am familiar with have removable circuit boards that have contacts which needs to be cleaned off once and a while and can cause the head to fail. Other than that I don't know. If the unit is on a timer, plug it directly and try it.