Signs Of A Dying Pc

It could have been the cooling pad instead of the external HD, or both. However, I've had this cooling pad for a while but that didn't happen in the past.

USB ports have a current limit that prevents (or at least tries to) burning out the main board / power supply when USB devices attached have a short, or use too much power.

There's a good chance that over time the fans in the cooling pad don't turn as lightly as before and startup current triggers the onboard protection circuitry, preventing your laptop from starting.

Try cleaning the fans, also turn them by hand and see if one of them is stuck. Replacements are cheap. They're probably sleeve-type, not ball bearing, so basically replacement is the only option.