Light kit was on and then just quit working. Fan blades no longer work either. Breaker is not tripped. Tested with a voltage meter and it is hot. Batteries in remote also work. Do I need to replace the receiver?

Where did you test "Tested with a voltage meter and it is hot"Do you see a small red light on the front top of the hand hld transmitter?

Sunday I had the receiver attached and the voltage meter I have does not need to be touched to wires, so it would beep when I held it close to the black and blue wires coming out of the receiver. After taking the receiver off the light fixture today leaving only the white and black wires coming out of the ceiling, the tester beeped when I placed it close to the black wire. I thought about wiring the fixture back without the receiver, however, I wasn't sure how to wire the black and white wire out of the ceiling to the black, white and blue wires coming out of the ceiling fixture.

That does not sound like a voltmeter, more of a voltage detector. For this kind of work you need a meter or test light. Black wire in ceiling box is your hot feed, should be hot unless this is also a switched feed, any wall switches? Black and white attach to black and white on the feed side of the receiver. Coming out of the receiver should be a black-hot to fan, white-common neutral for both fan and light and then another hot wire for fan. The light, most frequently blue. So with a tester or light you should get 120vac from the black and white in the ceiling box. Coming out of the receiver you should get voltage off the black and the white but only if you trun the fan ON via remote. You should also get voltage from blue and white but only if you turn on the fan via renote. Everything make sense so far?

What you have is a voltage sensor. It detects voltage on a wire by sensing the magnetic field around the wire. It tells you that you have voltage but it does not tell you that you have a complete circuit. Get a small Multimeter ($10-15). Set it to AC voltage and test for voltage between the black and white wires. If you do not get a voltage reading you have an open neutral. Then you can start looking for a bad connection in the white wire back to the circuit panel.