Sounds like it could be a connection problem. Hear's a simple test. Disconnect the leads to the cartridge (make a note of which wires connects with the cartridge). With your amp switched on. Touch with your finger (one at a time) each wire. You should hear a decent buzz on two of the wires - one wire for the right, one for the left. If you don't hear a buzz or it's weak, then there's nothing wrong with the cartridge, but either the cable between the amp and turntable is faulty or the amp's pre-amp has a fault. You can eliminate the pre-amp by switching the leads over. If the fault now goes to the other channel, it's the lead. But if it stays on the same channel, it's the pre-amp that's faulty.
If both channels buzz fine, then you either have faulty cartridge or a bad connection to the cartridge with the wire to it.