im having the same issue with my 2002 celica gt just one click and nothing did you ever figure this out?
Clicking can mean a loose connection between battery and starter. Follow wire to starter and clean/tighten connector at starter.
dead battery
2001 Toyota celice act like it want to start but won't can not get the window to go up
Battery is dead.
For Ignition. Your car will not start if this fuse blows, generally if there is a short.
1990 toyota celica when jumper cables are hooked up dash lights turn on but the car won't turn over won't even click
Did you check your starter?
It could have a leaky carburetor or injector that's causing the engine to flood.
Check your alternator and if that isn't it (but sounds like it) take a look at your starter.
Try changing the starter.
Check the battery cables. If there is no corrosion and you have good connections, then the starter solenoid/relay may be at fault.
The timing "chain"will start rattling at around the 100k to 110k mark. This is when it should be replaced