TRACON Controller reported that while providing training to a developmental; minimum vectoring altitude (MVA) requirements were not met; citing equipment issues as contributory.

Narrative

I was training a developmental (not my own and the first time I ever trained him) that had an extension of alloted hours. The purpose was to see if the trainee was ready for qualification; whereby I would let them go as far as possible. The Flight Data Controller had an aircraft waiting to depart a satellite airport IFR. The trainee issued runway heading and 3000 ft released. The pilot did not call airborne and the transponder did not acquire until approximately 7-8 miles north of the airport. No primary target was noticed either; (both Radars we normally use at this position were not tracking very well this day whatsoever). I called the pilot as soon as I had seen the data tag to see if he was on frequency and made initial radio contact. The aircraft was then climbed to 4000 ft and turned away from the antennas he was about to go into. The pilot was given 3000 ft with the expectation we would be in contact with him prior to the higher MVA (4000 ft) about 8-9 miles north of the field. It can be difficult to give a trainee enough latitude to let them demonstrate that they can handle a position yet not let them go too far. I let this trainee go too far (didn't see this situation coming; thought I would turn the aircraft if needed!). I would have had him issue 4000 ft to the Data Controller if under normal training circumstances