I just ran into and resolved seemingly the same problem tonight.
I had the same symptoms: no screen while touch sensor z wires connected. Once the 2 z pins were removed the screen turned on however I had no touch sensor pin self test activity on printer boot, touch sensor blue light was on though. Firstly, please note I have a 3D Touch sensor, not a true “BLTouch” and please consult your sensor instructions wiring details and verify things before blindly following my solution.
My problem was that the touch sensor supplied cable had some wires in the wrong order. I had to switch some wires around to work with the SV01.
With the sensor pin facing the floor and the connector facing me, my sensor had wire colors in the following order from left to right: (sensor expectations noted in parentheses)
Brown (Ground), Red (+5V), Yellow (Control), Black (Z), White (Z)
The 3 pin motherboard connector was originally supplied with INCOMPATIBLE ORDER: Yellow, Red, Brown
I had to switch a couple connector pins to the CORRECT ORDER: Yellow, Brown, Red
That way they are compatible with the D11 row pins:
(Power supply Side) Control, Ground, +5V (chassis side)
Simply changing the pin ordering corrected the screen issue and I immediately got self test pin activity from the sensor. I was able to run the printer with the touch sensor z wires connected.
I then had a new problem which was the probe would not detect properly and the hot end would plunge into the bed as there was no z limit from the sensor. Again my problem was the supplied 2 pin adapter for the motherboard also had the wires flip flopped. You may need to flip those wires too. Would encourage you to use the “auto home while holding an item under the sensor” method shown in the video above to verify the z limit is functioning before it tries to plunge through the bed (be prepared to turn off the printer if it flashes errors and tries to continue).