Just to be sure, you tried turning on the power at the wall switch and at the ceiling fan light switch, correct? No sense replacing a fixture if it's just an on/off issue.
Is this one of those where you have 1 wall switch that turns on the whole fan/light assembly, or do you have 2 wall switches, one for the fan, one for the light? If you like the light fixture, no sense replacing it, unless you'd rather have a different one, it's up to you.
1. Single wall switch: Turn it on and make sure the fan comes on. If fan comes on but no lights, problem is up in the fan area. If no fan or lights, problem might be in wall switch or fan area.
Fan comes on, no lights: Remove the light kit and verify none of the wires have come loose from any of the wire nuts. Black wires are 110v, white are neutral (return), green is ground. You need a good contact on the black wires, and the white wires, the green ground wires are just in case there is a short circuit, the electricity has a path to ground and not through you.
Pull on the wires a little, see if any of them are loose or come out. If so, tighten up the wire nut. This should fix it. If not, set a multimeter to 200v AC and check for 110V between the black and white wires. If it's there, the light switch may have gone out or socket has a poor connection in it and needs to be replaced. Either way, a new light kit will replace both. Make sure you get a good tight connection when you install the wire nuts, remember, keep the black wires with black wires and white wires with white wires.
Fan and lights don't come on:
Remove the wall plate and switch, be careful not to touch any bare wires or screws on the sides. Use a multimeter set on 200V AC, check for 110V between any white wire and the 2 black wires on the switch (one is power in, one is power out.) With the switch in the on position, you should see 110v between a white wire and either side of the switch. If not, turn off the circuit breaker to the branch and replace the wall switch. If you have power coming out of the switch, problem is up in the fan area. Follow the procedure above.
Congratulations, you have fixed your ceiling fan problem and are now a journeyman electrician.