Greetings,
Welcome to the forum.
I am not a HP employee.
Excessive dust can cause problems. Clean internals with compressed air or a dust buster. Let the PC sit for quite a while before reassemble and a power on test. Moisture and electricity are not a good mix.
Yes, the external power supply is a possible cause.
I would try starting the PC with only a mouse and keyboard. Then try starting the PC with no peripherals (mouse, keyboard, or printers, and external USB drives connected to the PC.
A system short can cause this issue. A short can be caused by excessive buildup of dust on the MB or components connected to the MB.
The short can also be caused by a peripheral device connected to the PC (bad port or bad device) or internal components connected to the motherboard.
I would start with the power supply after: a good cleaning and removing all external devices connected to the PC.
Work your way down to the motherboard.
Regards