Have a mate that has a 4AGE Twin Cam Corolla that has a weird problem where it basically won't run and sounds like it is misfiring, but EXTREMELY bad. Then if you turn the car off and back on again it MAY work fine until you turn it off again. Then turn it back on again and it may not work again.
Basically its a lucky dip if it will run fine or run like a bag of shit. It seems to do it a lot worse when hot.