It is almost always the RECEIVER batteries that go first... and depending on if you have the new model or the old model this will be either AAA's or CR2 which are readily available.
If the test button on the TRANSMITTER does NOT light up the LED on top, then it is most likely the tranmitter battery which is a 12 volt alkaline battery, type L1028 or 23A, of the variety used in smoke detectors and keychain remotes and the like. Its accessible by removing a small Phillips screw which keeps the halves of the transmitter shell together.
Before replacing the batteries, do as FITP says and take it out and check connections etc.
Hope this helps!!