I have experienced the same. I got my 05 OBXT last wendesday (used, 14800 miles). On the interstate yesterday, the radio and ACC screens went blank. Upon restart, they were back on. Then a few miles later, they went off again and didn't come back on with the restart. I tapped the radio screen and it then came back on.
Now today, I started the car to come back from my parents and they were off again. About 10 miles down the road, I tapped the radio screen a few times and it looked like the screens would partially come on for about 1 or 2 seconds. It stays off until I filled up the gas tank and then it stayed on the rest of my trip.
The radio and ACC both work fine other than the screen. I can change songs on the CD and adjust the ACC, just the screens stay off for a while.
Maybe I will have it checked out soon.