An IFR Cessna pilot suffered engine stoppage during the landing roll. Attempts to restart and exit the runway result in disorientation; temporary loss of control and a runway incursion.

Narrative

I completed the ILS 10R approach into Monterey Peninsula Airport. I touched down on 10R and during the rollout I pulled the throttle to idle. The aircraft was slowing as I approached taxiway Lima. Just prior to the taxiway the engine died. I attempted to start the engine by using the starter alone; without success. The Tower instructed me to clear the runway. I advised the tower of a problem with the aircraft. While going through a restart procedure where the boost pump was used; I heard the tower telling the following aircraft to be prepared for a go-around. I was able to get the engine started; but had the throttle in or at a high setting when the engine started. I quickly pulled the throttle to retard the engine causing the engine to die a second time. During the period of time that the engine was running I rolled onto Taxiway Lima. The engine started the second time with just the use of the starter. The aircraft was rolling during this time and I lost situational awareness of where I was on the taxiway. I thought that I might have entered the parallel runway; 10L. I continued straight to clear any runway and realized I had just crossed the hold short lines on to 10L. I was advised by the tower of a runway incursion; and continued onto taxiway Charlie to clear the runway. With tower progressive instructions I was able to taxi to parking without further incident. There were no other aircraft involved. While 10L was an active runway there was no traffic landing or departing at the time of my deviation. I felt that the incident was caused by my loss of situational awareness of my position on the taxiway. Contributing factors were the engine dying at idle while on the runway; a rushed improper restart procedure; and a concern about causing another pilot to do a missed approach back into IMC. The corrective action would have been to stop the aircraft once I realized I was unsure of my exact location on the taxiway and to request progressive taxi instructions.