A Tower Controller reported an aircraft deviated from their assigned SID and flew below the Minimum Vectoring Altitude.

Narrative

Aircraft X on the ZZZZZ sid off ZZZ Runway XXR on the south complex. Very light late night departure push. Aircraft X did not check in yet on Departure and I noticed that he was drifting northbound on the sid which should have been a straight out departure. Called local 1 to ask about Aircraft X and the response was 'i don't know'. By this time Aircraft X was pointed in almost a 320 heading and cut off the north complex and was not in radio contact yet. There are high MVAs north of ZZZ and ZZZ1 and the aircraft was headed right for them. Aircraft X finally checked in and seemed very confused. I gave him an immediate turn to the southwest and asked what happened. The pilot did not respond to that question. I gave him a climb and he responded to climb and I once again asked what happened on departure. At one point he said it 'dropped out' of the system. Both the pilot and I were confused about what happened and I was not receiving the information I wanted from the pilot about what happened.The worst part of this is ZZZ Tower's attitude towards the situation. They did not care at all; they did not verify the departure was on course and did not even notice he made an immediate northbound turn that would cut off the north complex. The only saving grace in this scenario is that it was a slow time in the evening and no planes were departing the north complex. If this had happened during a busy push it would have been absolutely disastrous. No MVA's were violated; and no loss occurred. ZZZ Tower lately has been doing things that has almost everyone in the area concerned and on our toes. They are becoming sloppy; dangerous and absolutely carefree about their operation. Suggestion: A change in the ZZZ Tower attitude towards a safe operation needs to emphasized to them