Toyota Repair: 1996 Toyota Celica wont start, toyota celica, engine fires


Question
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Followup To
Question -
1996 Toyota Celica (25th anniversary edition) was driving fine. Went out one morning & it wouldn't start. No clicks, wont turn over, nothing! Took battery to be checked out. Battery was bad. Replaced with Sears diehard. Still nothing. Starter had been replaced 6 months ago. Took starter to be checked out. It was fine. Replaced ignition switch and starter relay switch. Still nothing. Lights are strong. Any ideas? Thanks!
Answer -
If it is a manual transmission there may be a problem with the clutch start switch, if it's an automatic the problem could be in the neutral start switch located on the transmission, another possibility could be a problem with the alarm system, if so equipped,give me a liitle more information.

More info:
It is an automatic with an alarm system. I turned off the alarm switch under the dash left of the drivers seat. It didnt seem to cut the alarm off though. What should I do next? Thanks!  

Answer
Tahnks for the additional info, try disconnecting the negative battery terminal, open the driver side door and put the ignition key in the ON position, leave the door open and reconnect the battery, do not turn the key off but turn it directly to the start position and see if the engine fires up, this works with some, but not all alarm systems.