No USB connected, receiving error message "USB devices disabled: Unplug the device using too much power"

This could be a hardware problem.

You have more things connected to USB than you are aware of. Looking at the "System Profiler" under the "USB" section, we see a number of things:

• FaceTime Camera
• Bluetooth
• Trackpad*
• Keyboard*

^{* Not shown because I am on an iMac}

There could be an issue with any/all of these devices or there may be an issue with one of the power rails (the circuit that delivers power to these devices).

First thing to do is run Apple Hardware Test (AHT). Hold the D key while booting from a powered off state with the AC adapter connected. Next, try running things in Safe Mode (hold Shift while booting). If the problem persists, the issue is definitely hardware.