Sorry if this is too obvious, but the BBW won't do anything without a micro SD card plugged in, do you have an SD card with a fresh image loaded and plugged it before powering up?
The BBB has an eMMC "flash" preloaded, so its likely dead if the previous owner didn't break the boot by messing with uEnv.txt or something else. Still I'd try a fresh SD card on it too before giving up.
I've not found them to be particularly fragile with respect to just pulling the plug when things have frozen -- no keyboard/mouse response, no SSH login. They are pretty fragile to probe slips when measuring the GPIO pins if things short to power or ground.