A single USB port not working is definitely a MoBo issue, but by "mobo issue" it could be nothing more than that single port died. It's not necessarily indicative of a larger problem (for example, my mobo only has usb 3.0 ports, but no matter what I do it will only recognize them as 2.0). If you're really hurting by losing that port, just get a powered hub (they're super cheap).
The booting issue is almost definitely not related to the USB port. As far as the booting/shutdown issues, it really sounds like an OS problem. If it won't initialize the restart/shutdown procedure from the desktop, and it has trouble cleanly booting to the desktop, but is able to get past POST, that's where I would start looking.
If possible, try either repairing the OS from the restore utility, or reinstalling altogether. If you really don't want to lose your data, you could install Windows to a clean drive (USB or w/e) and see if you have the same issues.