A TRACON Controller reported a GA aircraft running out of fuel and disoriented descended below the Minimum Vectoring Altitude. The Controller reported an adjacent sector vectored the aircraft 20 miles out of the way of their destination and the Supervisor on duty did not assist.

Narrative

Aircraft X attempted 2 ILS approaches at ZZZ and reported unable to capture the localizer and was disoriented in the IFR conditions. He stated to the P Controller that he needed him to keep an eye on him; he wants to go to ZZZ1 and do a visual approach; he is low on gas and in IMC conditions. The P Controller puts him in the data block but neither he nor Aircraft X [request priority handling]. As the receiving controller and the controlling authority for ZZZ1 I inquired about them headed my way.I was told: he's disoriented; can't hold his headings and low on fuel [and] just needs priority handling. The P Controller vectored him 20 miles north of ZZZ where another pilot had reported VMC conditions at 3000 ft. The final controller offered Aircraft X to use that airspace but another aircraft was on an instrument approach to ZZZ and Aircraft X was being vectored around him. Aircraft X was handed off to me on the L position and the P Controller coordinated on the landline Aircraft X has trouble holding his heading; trying to get to ZZZ1 and is low fuel. Aircraft X keyed up on my frequency and said I need help; keep your eyes on me; I need the frequency for ZZZ1. I gave him the altimeter 29.92 and asked if he wanted an instrument approach or a visual approach and he responded visual approach. I told Aircraft X it appeared he was heading about 20 degrees southeast of ZZZ1 and he asked for a heading. I gave him heading 100. Was descended to 2000 ft. To swap altitudes with another aircraft inbound for ZZZ2. I gave Aircraft X the CTAF frequency for ZZZ2 and confirmed that he had received the correct frequency. I called the field location 12 to 1 o'clock in 10 miles he said he needed lower and I told him my MVA for his area was 1700 ft. And he said he needed lower and was not out of the bases. He said I don't want to miss I can't go around. I told him the field was at 2 o'clock in 5 miles.I asked if he could provide his own terrain and obstruction avoidance. He said he could but still could not find the field and asked to descend. I told him I could not issue a vector below the MVA and which runway did he want Runway XX or XY and I told him to fly heading 090 to put him on a 2 mile base leg for the field. I [declared priority handling] for him and asked how many people were on board and how much fuel. Aircraft X stated 3 people and 5 gallons of fuel. He had started descending for the airport and said can you help me? I told him as long as he could provide his own terrain and obstruction avoidance; he needed to turn to the southwest as the airport was now behind him. I observed him at 800 ft. Around this time.During this whole time I was asking for help in the room from the supervisor or anyone else; what else could I do and it was not until XA25 that finally the P Controller showed up behind me.Aircraft X continued to state he could not see the airport. I asked another aircraft on my frequency Aircraft Y to go to CTAF and try to turn the lights on for Aircraft X and see if he could hear Aircraft X who was now observed at 400 ft. Circling the airport. Aircraft Y said he could hear him clicking but it wasn't turning on the lights. Yet another aircraft on my frequency said he was able to get the lights on for Aircraft X. Aircraft Y said he heard Aircraft X on the CTAF frequency and he had the field in sight and was going in to land. I thanked Aircraft Y and asked him to relay the phone number for the TRACON to Aircraft X and have him call us. I then gave up the position to the P Controller. The supervisor asked to see me and apologized for not being there to help me and said he was unaware that the situation was so serious. That another controller on the south satellite sector was needing another set of eyes on his traffic. I said ok and left the room. On the weekend after a break; we needed more staffing and possibly an overhead coordinator to be able to provide assistance so the supervisor could help the [priority] situation.I asked for help repeatedly and all my calls fell on deaf ears. The P Controller did not heed the sense of urgency and fear from the pilot and needlessly vectored him an additional 15 to 20 miles out of his way rather than [giving priority handling] and letting him go direct. Also; put an aircraft not in distress and going farther (ZZZ2) on a vector and altitude to go underneath Aircraft X which would have further prevented him from descending. We need a better sense of urgency in low fuel situations especially with a GA pilot in IMC conditions.