Look at the BIOS parameters before boot, there should be an option to enable/disable the Usb EHCI (enhanced host control interface). As far as I understand it is enabled by default, but a previous user may have disabled it.You can obtain basic diagnostic information from the Windows event log, and since you have access to an oscilloscope you might want to try a tool for Usb electrical analysis (see http://www.usb.org/developers/tools/).
One thing to consider is what version USB ports do you have? I've had problems using my Leonardo on USB3.0 ports. I had to move it to a USB2.0 port to work correctly.