Ceiling heater in bathroom is broken.. how to fix?

If you are not familiar with electricity and electrical safety, hire an electrician. Before I would replace the heater, though, I would make sure it is getting voltage after the timer is turned on. The timer may be bad. Your electrician needs to check voltage on the source side of the timer first. If no voltage, check the breaker at the panel. If voltage is present at the timer, turn the timer on and check to see if voltage is present on the load side of the timer. If it is not, replace the timer. If it is, the next step is to check voltage at the heater. If voltage is not present at the heater, check all connections between the timer and the heater. If voltage is present, and all connections to the heater is good, then it may be time to replace the heater.
Good luck.