B737 Captain reports applying the MEL procedure for a failed left ignition while the right ignition had actually failed. The MEL requires an operating ignition be connected to the AC standby bus for dispatch.

Narrative

On taxi out; engine did not light off during start. Aborted start and parked on ramp to troubleshoot. Before taking any action; I called our Dispatcher on my cell phone and asked him to get maintenance Control on line to discuss the problem. I described the problem and asked if we could operate with the condition while I looked up the MEL item and allowed starter to cool. I thought I told him that it was the #1 engine; right ignition. He told me to select the other ignition and if it started; go to the flight position and operate it in that position for the flight. By that time I had the MEL book open to the correct page and was reading along with him. The engine started and we took off in that condition. At cruise; I pulled out the MEL book to review and realized that we applied the procedure for the left ignition; not the right. The correct MEL was condition B and called for maintenance to swap ignition sources. I contacted dispatch by ACARS to point out the error and set up for maintenance. Contract maintenance corrected the ignition. Somehow maintenance misunderstood which ignition source we had a problem with. I don't known where the communication failure came in. I wonder if I incorrectly called the #1 engine the left engine and confused him. We followed the procedures; but by the time I had the MEL book out; the Maintenance Technician was reading the procedure and I fell in with him on the wrong condition. Since we seemed to be in agreement; I did not have the First Officer review the MEL with me which is my usual habit while applying an MEL at the gate. This removed a barrier. Our MEL book can be very confusing and since I have received several aircraft with the wrong MEL applied; I try to read the book very carefully. We had 4 logbook write-ups before leaving the gate resulting in 2 MELs being installed just prior to pushback and a late departure. I guess I was getting in the yellow and just didn't take enough time to carefully read the procedure. Our MEL procedures need to be reviewed. The MEL book is very cumbersome; with many different items covered in the same MEL number. The 737 fuel gauge MEL is a good example. It is several pages long; covers several different aircraft configurations and for certain tail numbers requires a FR logbook entry. I don't remember having this many problems with our old MEL system.