PC only power-cycles after a USB mouse cable shorted

The repeated fan spin is a failed power-on self-test, so the next step is hardware isolation. Disconnect drives, add-in cards, and USB headers, then test with the motherboard, CPU, one RAM stick, and the power supply. Diagnostic LEDs, a speaker beep code, or a POST card can help identify whether the failure is related to memory, CPU, or the board.

Resetting the CMOS is worth trying before buying parts. Disconnect the AC power, remove the motherboard's coin-cell battery, and use the clear-CMOS jumper according to the board manual if one is available. After waiting a few minutes, reinstall the battery and reconnect power. This probably will not repair burned hardware, but it can rule out corrupted firmware settings.

Do not assume the motherboard is definitely dead yet. A failing power supply, a damaged USB protection circuit, or a short involving a case USB header can all produce this behavior. If possible, test with a known-good compatible power supply, and inspect or disconnect the front-panel USB cables before considering a motherboard replacement.

A shorted USB cable can trip the port's protection, but whether it causes permanent damage depends on the motherboard and power-supply design. The visible USB socket can look normal even if the port controller or protection circuitry was damaged internally. Try disconnecting the damaged mouse completely and test the system with only the essential components connected.