First of all Ive got a Pixhawk with the PX4 firmware. At the beginning I used APM. During that time there were no problem connecting Mission Planner to the Pixhawk via 3DR Telemtry Radio. But I had to change from APM to PX4. When I want to connect them now it doesn’t work. Both Radio modules are solid green, but i doesn’t work. I read that some people tried to downgrade the FW(i’m not sure which FW they mean), but isn’t there another way?
When you say it was in use on an APM2.x did you change the cable that was in use? Just that from memory an APM2.x has a 5 pin connector and the Pixhawk / PX4 has a 6 pin connector.
I’d suggest firstly checking that you have the wires connecting to the right pins. You’ll get a green light if both radio’s are on the same ID and powered up. If you have the TX and RX around the wrong way but the GND and +5V are wired correctly it will do what your describing.
Another thing is to try using MP and connecting to the radio and checking that the two are the same. Swap them over if you have V2 radios.
Do you have a MinimOSD connected as well? If so does it have both TX and RX connected, if on the same port as the radio it should only have the RX connected.