No reverse? Radiator was changed

Running it low on fluid may have made the reverse clutches burn up. There are two shaft speed sensors which may not through a code when they are bad, turbine and intermediate. Here are the locations in case you want to try changing them out. Also, you may want to drop the pan and install a new filter and fluid to see if that helps. Here is a guide to help walk you through the service:

https://www.2carpros.com/articles/how-to-service-an-automatic-transmission

Check out the diagrams (below). Please let us know what you find. We are interested to see what it is.

The clutches being bad is what I was thinking, but I was hoping I was wrong. When he first brought it in, the reason was that he said it seemed it was revving up more. The trans was only one quart low. I pulled the radiator cap and found the fluid in there. He replaced the radiator and lost fluid when he did that. He said it was running fine, then the reverse thing happened. I rechecked the fluid and it was only two quarts low. On the scanner I have no codes. I am reading that it is going in every gear, but when I put on the brake in reverse the slip ratio and shift speed still have readings. They should go to zero. They go to zero in all drive gears. I am checking this with all wheels off the ground. It did turn the wheel in reverse when in the air. I don't think it is a speed sensor. The oil is clean and red, I don't feel it is a simple service. Do you still feel it is the reverse clutches?

Yep, it sounds like the reverse clutches are burnt up, so are you saying you have transmission fluid inside the radiator? If so, the radiator needs to be replaced and the cooling system flushed, this also means coolant could have gotten into the transmission and caused the issue along with the low fluid.

Thanks.