A bad ECU (ECM PCM, whatever you want to call it) can be hard to diagnose, but cause all sorts of wierd problems. Sometimes, it'* easiest to diagnose by swapping a known good unit in and see what happens.
It is under the passenger side of the dash. You have to remove the black kick panel from above the passenger foot well to get to it. You'll have to lay upside down to see it. It has three connectors on it, and is held up by one metal tab and a bolt, then you have to wiggle it at just the right angle to get it out. In my opinion, it'* worth a try. But don't pay for one before testing unless you are sure you can return it.