This is a really strange issue. I’m not sure how it could’ve hsappend while homing, unless perhaps there’s some kind of intermittent wiring short.
I suspect you heard when the board died- and you did the right thing to power down at that point.
When 3V3 isn’t present, the processor on the SKR is dead.
If you want to troubleshoot further, I’d measure the 3V3 and 5V rails with and without the SD card in.
You could also try only connecting marlin mode and only connecting TFT mode cables to your display. The two grey cables are only used in Marlin mode, the black cable is only used in TFT mode. The TFT should power up with either the black cable (only) in, or the two grey cables in.
It would be interesting to know what the TFT does with either config, with and without the SD card in (4 tests)