TRACON Controller reported an aircraft went around; but then did not listen consistently to the Controllers instructions leading to a Minimum Vectoring Altitude violation.

Narrative

I was working arrivals to Runway XXR. Aircraft X initiated a go around short final. I issued them a turn to 240 and 9;000 feet as local center was departing and I wanted to give them room. Aircraft X read back the instruction but did not turn and leveled off about 5;400 feet. I instructed Aircraft X to turn further right heading 280 with no response. I issued multiple headings further and further to the northwest to avoid terrain and sometimes they would respond and sometimes they would not. I asked multiple times about their altitude and instructed them to climb however they flew level around 5;400 feet for about 5 miles. I was doing my best to turn them away from rapidly rising terrain as it became evident they weren't climbing; but may have still gone into a higher MVA southwest of the airport.I believe the flight crew was dealing with some type of malfunction or abnormality were talking to me was not their priority. In hindsight I could have issued a low altitude alert to try to alert the crew they need to turn and climb in a more timely manner.