I recommend that you double check that model number and make sure that you have the correct electronic control board installed in the dryer. The part number of the control board for model 110.87571601 should be W10111606.
If the correct control board is installed, then you could have a bad replacement control board or another problem that is preventing the control board from working properly. On a few of the HE types of dryers, there has been an unusual issue that has caused some intermittent F01 error codes. A short in the moisture sensor wires has been known to cause this error code. I provided a wiring diagram for this dryer in the image below. You can
unplug the dryer
and access the control board. Unplug the moisture sensor wires from the control board and then reassemble the dryer. Power it back up and see if you still get the F01 error code. If not, then I recommend that you carefully check the moisture sensor wire harness for a short to the metal cabinet.
There is a possibility that you have a bad touchpad that is causing this problem. If the above steps don't help, you may need to try replacing that component.
I hope that these tips help. This may be a difficult failure to diagnose. If you do not feel confident repairing this problem yourself, then you can have it repaired at your home by a Sears technician. Here is a link for the website:
Sears Home Services
If you need more help, reply with additional details and we will try to assist you further.