Tower Controller reported ground conflict when a departure was cleared for takeoff with traffic crossing the runway downfield.

Narrative

There was above average volume for most of the morning shift. Due to a Controller calling out sick we had less than ideal staffing on the shift; which required all the Controllers working that shift to take shorter breaks than normal. We began running delays a few hours into the shift. Managing the demand was difficult due to the Line Up and Wait (LUAW) rules in effect at ZZZ. We had a need for LUAW but were unable to use it most of the morning due to staffing constraints. In addition to extreme departure demand Runway 1/19 was closed most of the morning for maintenance; leaving us with just one runway for arrivals and departures. As the end of my shift approached it was required that I stay for overtime to keep open all necessary positions.At the time the first Controller got in for the afternoon shift I was working Local Control and CIC combined. When she arrived I assigned her CIC gave her a briefing for the position. Splitting off this position allowed us to begin utilizing LUAW procedures. As I approached 2 hours on position the CIC offered to recombine the positions to relieve me. I volunteered to stay on position until more relief came in for the night shift. This would allow us to accommodate more departures and help with the mounting delays. At around XA40Z I instructed Aircraft X to Line Up and Wait on Runway 24 to hold for spacing with the previous departure. The Ground Controller coordinated for a crossing at the intersection of Taxiway G and Runway 24 which I approved and told him traffic would hold in position on Runway 24. Shortly after he requested a second crossing of Runway 24 at Taxiway C. I also approved the second crossing request. After the first crossing at G was completed I scanned the radar to check for spacing with the previous departure and scanned the runway at which time I cleared Aircraft X for take off. Right after Aircraft X began departure roll ground yelled at me to 'stop'. I immediate looked up and saw a twin prop crossing Runway 24 at C; I had forgotten about the approved crossing. I keyed the mic and issued instructions for Aircraft X to cancel takeoff clearance and stop. After the situation was over I turned Aircraft X off the runway and issued instructions back to the Active runway. The CIC then relieved me and recombined the positions.The cause of this situation was my forgetting the crossing and my missing the crossing during my scan. I need to analyze both my techniques for remembering crossings as well as improving my scanning techniques to both ensure that I don't forget crossing and then in the event that I do my scan catches any similar situation before is occurs. I also think the fact that I had been working busy traffic most of the day with short breaks and volunteered to stay on position longer may have played a role. While at the time I declined a break I felt capable of working; once I was 9 hours into an 8 hour shift that started early in the morning and had been on position for over 2 hours I probably was not performing at 100% which likely contributed to my memory lapse and degraded my ability to scan. In the future I think it would be better to have taken a break even if just a short one to 'recharge my batteries' when one is available.