Beechcraft F35 pilot reported engine failure on takeoff and a resulting runway excursion.

Narrative

We flew up to ZZZ [airport] for lunch. At lunch noted an aircraft that landed high and fast. After lunch we started to get ready to depart. When doing my run up some airport personnel noted that the aircraft was off to the side of the runway. They said that I could taxi to Runway XX and use the runway past where the aircraft was. I was nervous as I don't like being around incidents. I finished the run up and taxied to runway XX. I had a passenger with me and was a bit distracted with his presence. I then realized I hadn't done my before takeoff checklist. I haphazardly did the checklist as simultaneously an aircraft called inbound to land on runway XY. Now I was concerned that being at an uncontrolled field that this guy could just come in and land on the runway I was taking off on. Now I was even more rushed. I taxied abeam the disabled aircraft - there were no vehicles or aircraft the runway.With 3000' of available runway I had plenty of room as my aircraft usually has a ground roll of about 800'. I applied full power; and we climbed out. At about 100' AGL we lost engine power. I checked throttle/prop/mixture; and did not have much more time for anything else I flew down to the runway; landed firmly and applied maximum braking. Right at that moment; the engine power came back and I immediately pulled to idle and continued braking. We departed the arrival end of runway XY at between 5-7 knots approximately; hit soft dirt and a ditch.After stopped I found that the fuel selector was in the Aux Tank position which were about 1/3 full. The fuel pickups in those tanks are in the forward part of the tank. When climbing out they became un-covered. Upon landing they were covered again.Contributing factors was that I was uncharacteristically rushed. I was distracted by the attendance of my friend as he is a pilot as well. The accident had me rattled; the inbound aircraft; and not doing my preflight checklist in a methodical manner.I am so ashamed of myself with this; as I said it is so different than I would usually behave. I actually wanted to pull to the side and let things settle out before taking off. I have deep regret.