This is one of those times when "bad grounds" is not just a one-size-fits-all solution to electrical problems. Seems highly likely to me.
This would be a good time to buy a cheap multimeter, or at least a test lamp, and start practicing troubleshooting--trace through the circuit to see where you are losing voltage. Check for voltage at the lamps, and if they have no voltage, continue up the circuit toward the source and see where you are losing it.
By the way, don't assume that the problem isn't simple. Are the bulbs OK? Are the socket contacts clean? Seems unlikely that more than one bulb would die at one time, but coincidences do happen sometimes.