B737 flight crew is cleared to cross Runway 24L and cleared for takeoff on Runway 24R. Crew turns on Taxiway C and attempts takeoff before being informed of error by Tower Controller.

Narrative

Crew delayed on ferry flight departing CLE. Crew felt somewhat rushed due to need to get airborne for long day ahead. Taxi clearance was 'via Taxiway J to Taxiway S.' Approaching Taxiway S; Ground Control instructed 'cross the left (which was closed for maintenance); switch to Tower holding short of the right.' Pilot Not Flying switched radio and was reading checklist. Tower transmitted 'traffic on 5 mile final; cleared for takeoff on the right.' Pilot Not Flying read back clearance. Both pilots looked toward the final area and observed lights. Pilot Not Flying went head down to finish checklist items. Pilot Flying made left turn and started to add power. Tower transmitted 'stop! You're on a taxiway.' Pilot Flying stopped aircraft. Pilot Flying had turned onto parallel taxiway between runways. Tower then cancelled takeoff clearance and gave taxi instructions. Very alert Tower Controller prevented a very serious incident. Crew is very experienced but not familiar with CLE. Taxi diagram is very cluttered. Pilot Not Flying had diagram on yoke clip and giving directions to Pilot Flying. After crossing the left runway on Taxiway S; neither pilot noted the parallel taxiway between the runways. Contributing factors: rain; reduced visibility; poor airport layout. Crew received takeoff clearance quicker than expected. Crew not familiar with airport. Crew desire to 'get the job done.' Both Pilots are 'Captain qualified' and have flown together for many years.