After landing on RWY 31L, the aircrew of N100VV requested clearance to turn off to the right at midfield onto RWY 22. The request was approved and the aircrew was instructed to use caution for a Cherokee proceeding from the opposite direction. The pilot of N100VV stated that after he turned right onto RWY 4/22 and was clear of the Cherokee, he attempted to contact the tower to advise of his intentions. However, the frequency was too busy, so he switched to the ground frequency and transmitted that he was 'off 31L, going to Atlantic.' This transmission ended just as N100VV was entering the intersection of RWYs 22 and 31R. Just prior to that, N222WL had been cleared for takeoff on RWY 31R and had begun its takeoff roll. N222WL was at approximately 70 knots when its aircrew saw N100VV starting to cross the active runway. The pilot of N222WL attempted to take off and avoid a collision, but was unable to clear N100VV. N222WL crashed and slid to a stop approximately 400 feet beyond the impact point with N100VV, then burned.