as we were pulling away from a stop sign, there was a fairly loud whining sound and then a thump,like you would have maybe run over something. the vehicle started to slow down and there was no power.

because I don't know you mechanical knowledge base, I will firstly state that you should never shift in to reverse/drive while traveling in the opposite direction. with that said if this has been done multiple times you may have a transmission issue or it could be as simple as you transmission fluid is low or needs replaced.

Is the power steering fluid low? Sometimes a low growling noise coming from the PSB will make the engine bogg down

The whine could be power steering pump low on oil but not moving... that sounds like you may have broken an axle or u-joint. Jack up rear end and turn one wheel by hand. while it is turning, see if the other side is turning. If not, you broke an axle. If that is not it, while it is up in the air, look under the car and see if the drive-shaft is connected at both ends.

If it is a power or transmission issue, then it should have lights on, on the dash telling you that you have an engine or trans problem. Being it is a 5R55 transmission, it is possible that your transmission has given up the ghost. It is a common happening for a high mileage Explorer to have this problem. I don't know your mileage, but am guessing it is up there. Above the radio are a set of switches on the left. Have you tried them to see if maybe the shift motor has gone out on the transfer case? There are so many possiblities, that without some other information, we can only guess. I'm thinking that it is powertrain related, and not computer or electrical. Good luck.