A Tower Local Controller reported they cleared an aircraft for takeoff with a taxiing aircraft crossing the departure end of the runway.

Narrative

I was working Local Control. It was very busy. There was training on Ground Control; training on Clearance Delivery; a CIC (Controller In Charge); and several other controllers in the Tower not on position. The Ground Control coordinated a crossing at the departure end of the runway for a gap that was 2 miles away (2 min flying time). I told them it was approved and I would have a jet in position for the crossing. At the appropriate time; I placed the jet in LUAW (Line Up And Wait); and used a memory aid hung over the departure strip to remind myself of the downfield crossing. I went to other sequencing tasks; and was alerted by several controllers in the Tower that the jet was rolling before the cross was complete. I cancelled the jets take off clearance in time; and they exited prior to the crossing aircraft. Upon review of the tape; I did in fact clear the jet for take off. I am unsure how; and have no recollection of doing this. The S.A.I.D. (Surface Area Information Display) for the Local Control position was out of service. There were numerous distractions in the Tower environment; including conversations about the current shutdown; double training; and lots of background noise.I do not know how to prevent this other than limiting personnel in the Tower cab to only essential people who are on position. The stress of not knowing when I'd be paid was a contributing factor. I was working my 3rd unpaid overtime shift since the shutdown began when this incident occurred