No longer able to program my NUCLEO-H743ZI
I guess it’s not impossible for your four cables to be bad, but it is unlikely; if they work with some other peripheral then it’s pretty much looking like your NUCLEO...
Looking at the data sheet for your board, it doesn’t appear there are jumpers that could be causing this.
I would guess that the two most likely things are either you cracked the tracks on the USB connector on the NUCLEO (just physical wear and tear) _or_ you zapped it somehow (ESD)
The software wouldn’t just die, and anyway as I mentioned the micro that does the ST-Link isn’t the STM32H743 that you are programming.
Can’t do much about ESD damage but the cracked tracks would be discoverable and repairable if you have a multimeter and a fine soldering iron... but personally I’d triple check maybe with a fifth cable and another computer (eg: linux box with lsusb) that you’re sure it’s not something simple before going at it with the tools...