Here's some stuff to try...
* Make sure that the battery contacts in the transmitter (the handheld part) are clean and not bent/broken and making good battery contact.
* Try a different set of batteries in both the transmitter and in the reciever. The odd bad or dead battery could cause your symptoms.
* Be sure the crystals are firmly plugged into both the tx and rx (transmitter & reciever).
* Be sure the rx antenna is not cut or pinched against a metal surface.
* Be sure that the servo and battery plugs are pushed firmly into the rx and that none of their wires are cut or pinched against something metal.
* Check the battery holder for the rx to be sure the contacts are clean and good and that the plastic case is not cracked or broken.

If none of that helps, then you may have other, more serious radio problems. It is just a piece of electronics after all and could simply fail. In which case I'd check with the folks you bought it from (or the manufacturer) and see about warranty repair or replacement.
Good luck