ADS Controller described pilot deviation event when departing traffic initiated takeoff without clearance and with traffic on short final resulting in less than required separation.

Narrative

I was working Local Control. It was after sunset. Aircraft X called ready for departure on Taxiway A holding short of Runway 33. Aircraft Y was just touching down. I cleared Aircraft Z; about 5 miles southeast of the field inbound; to land. Multiple aircraft responded; and I could not determine who had said what. I requested that the aircraft verify that Aircraft Z was responding to my transmission. Aircraft Z read back the landing clearance again. Aircraft W; entering the right downwind; was then instructed to follow Aircraft Z 5 miles southeast of the field and advise when he had the traffic in sight. By this time I looked at Aircraft Y; who appeared to be slow enough for runway exiting instructions; which I issued at that time. Then; while scanning the runway from departure end to approach end I issued the hold short instructions to Aircraft X. During my scan and my transmission I saw the light of an aircraft rolling on the runway about 1;500 FT from the approach end of Runway 33. Aircraft X did not respond to my transmission; and I could no longer see Aircraft X holding short of the runway. I notified the other staff in the Tower; and we watched Aircraft X depart and tag up while Aircraft Y was still on the runway. I issued traffic to Aircraft X and Aircraft W who appeared to be a conflict as Aircraft X was turning right to heading 090; and Aircraft W was just east of the field in the downwind. I asked Aircraft X; a student pilot; if there was an instructor on board. He advised me that he was attempting a student solo flight. Aircraft X and Aircraft Y were on the runway at the same time; due to Aircraft X taking off without a clearance. I would estimate the distance between the aircraft somewhere between 5;000 FT and 4;500 FT. Recommendation; I think this event was caused because the student pilot had little experience. This person may have been distracted or nervous; as many people without experience seem to be; and his actions indicate that he missed some important clues. The pilot should have listened carefully to the controller's instructions; because his call sign was not mentioned in the clearance he misunderstood. Also; when I requested verification that the correct aircraft had taken the landing clearance; the pilot did not seem to hear it. Last; when Aircraft Y landed and while Aircraft X was taking off the Falcon was rolling down the runway in direct line of sight of the pilot; I think he should have taken the time to clarify what he thought he heard before taking off. I think all pilots...especially student pilots; should take the time to have the controller reissue any instructions they are not sure about; and pay close attention to what is going on around them. The few seconds it takes to do those 2 things could probably save many lives.