Only a few items to cause the problem.
1. The bulbs all blew at the same time and need replacing ( it does happen believe it or not)
2. The pull chain has failed with the contacts open, cycle and then test the pull chain switch with a voltage tester or bypassing it with the wiring
3. The wattage limiter has failed.
The wattage limiter is new item that the govt requires for fan light assemblies to limit the wattage used on bulbs.
Unfortunately, they fail very often and hard to get new ones.
CLICK HERE for one of the few places that can get the wattage limiters.(go to the middle of the page and you will see the "limiters")
The only way to find out, is test the wires to the lamp sockets unfortunately on the wattage limiter.
You can remove all but one bulb and see if ti starts to work of even a flickering of the bulb will point to it as bad too.
I have seen them work fine with one bulb and die when the 2nd one is installed, they are truly finicky and real problem in many cases.
They cannot be bypassed due to the danger of overlamping and UL safety.
Let me know any clarification needed or added info, here to help get it going with you,