strange turtle of death behavior

i have a gen 1 2002 prius. second owner. bought in march 2005 with 65K miles, now it is may 09 and i have 140K miles. I am buying a 2010 3rd gen package 4 with solar nav in (hopefully) late June.

i have had a very good experience maintenance wise - no unusual issues.

the car has a wierd habit, though. If i sit in a parking lot waiting for someone, and i use the key to momentarily power a window or something, or if i put the key in and turn it in a funky way, when i start it up i get the triangle and turtle. The first time it scared me s-less, as the manual said don't drive - tow asap. I have learned over time how to deal with it. When i get the screen, i shut if off and on until the motor kicks on when i start it (the first few times the motor doesn't come on and it is almost undrivable). When the motor kicks on it is drivable but not normal or safe. I drive it 5 or 10 seconds, stop, and restart. Then its normal but the warning lights stay on until the next day. This happens 3 or 4 times a year, and always after the waiting situation. It may have something to do with me sitting in the car.

Anyway - any experiences like this? Any fix short of replacing the "computer"? What does that cost? This situation will keep me from selling the car to anybody i know - i will trade it in instead, but that will just be passing this problem on to the next person.

thoughts?

 

thanks for responding john. i get the turtle and the triangle. the battery is usually at half or less bars when this happens. when i start the car, the ice does not start. i restart until it does, then it drives wonky and unsafe. then i resrat again and it drives ok.

i replaced the little battery at 105K miles (35k miles ago) - and i THINK this issue predated that but now i can't be sure