Just what I found from way back when..
My 1990 Celica with a 5sfe 4cyl engine had a crack in the coil. I couldn't see it until I removed the coil and started really looking at it close...in the cold or wet the car wouldn't start and I would kill the battery cranking the engine. I ended up switching out the coil, (the crack was in the epoxy coating) and I NEVER had another problem starting it.
Just from my experience on that engine....since the 5sfe, 1mzfe, 3mzfe are so common of engines I thought I might chime in.