'96 dodge intrepid randomly shuts down @ 40-50mph?

This doesn't happen all the time, and it's definitely not predictable. I'll be driving along fine and then accelerate to 40 or so, and the car just shuts off. All my gauges are still lit up, so i know i have power, but trying to turn the car back on won't work. I have to pull over and let it sit for a few minutes, and then it starts right back up. I was having a previous problem with my battery, where one of the connectors (?) was corroded so that the tip doesn't always touch the battery. Sorry, that's the best I can explain it. Would the battery connections force the car off at certain points? The car has shut off once or twice when I was below 40, but mostly it's 40mph or above. Any help would be appreciated. I know I ran a diagnostic a while back and they said that there was a carbon buildup somewhere (I don't remember the exact error code, but it was a check engine warning light), that would limit my performance at medium speed, probably around 40. Any ideas?