Yes, the basic "is it detected as a USB device when plugged in"
Turn on your speakers and turn up the volume.
Unplug the USB of the printer while powered and plug it into a known working USB port.
Does Windows Ding loudly when the USB cord is plugged in? Is so, is it the good ding- driver loaded, or the bad ding- oh crap, device unrecognized.
NO ding either means your USB cord is bad or the 8u2 USB to serial processor on the mainboard is dead (most likely) or in a rare attempt, you could attempt an AVR programmer to try and flash it.
Given the 8u2 AKA USB to serial IC is the most voltage sensitive and blows at ANYTHING over about 5.53V likely it's dead and the repair either way is a royal pain.
you are either looking at a replacement mainboard or a very difficult surface mount IC replacement- and then you still gotta flash the bare chip.