The P8 plug you removed supplies the +12 and -12 volts to the 5150/5155/5160 motherboard.
CONCLUSION: Because the fan is now turning, and before it wasn't, we now know that your motherboard has a short-circuit in either the +12 or -12 volt lines.
What Now?
It is very highly likely that either a tantalum capacitor on the +12 volt line or a tantalum capacitor on the -12 volt line of your motherboard is short-circuit.
A short-circuit tantalum capacitor on a 12 volt line is a very common problem with the 5150/5155/5160 motherboards (well, ones that have not been used in a very long time).
Visually inspecting the tantalum capacitors may (repeat: may) reveal the faulty capacitor.
In some cases, the faulty tantalum capacitor is very obvious.
In some cases, the faulty tantalum capacitor may only have a small black eye/hole.
But the faulty tantalum capacitor may have absolutely no visual indication of failure.
If there is no visual indication of failure, proceed to the appropriate section below.
5150 motherboard (PC) - type 16KB-64KB
Click here.
5150 motherboard (PC) - type 64KB-256KB
Click here.
5155 motherboard (Portable PC)
The 5155 contains an early 5160 motherboard. Refer to the 5160 motherboard section that follows.
5160 motherboard (XT)
Click here.