Without the CPU fan running ,the CPU is overheating and not allowing you to boot. If the fan wire is disconnected, connect it. As far as removing the fan+heatsink, go ahead. A tiny tube of the special heat resisting gunk for the processor is only a few dollars.
However,that is not the obvious problem alone if your computer is not only NOT booting but NOT shutting itself off from overheating. Your hardware CMOS is out of sync. To reset the CMOS to factory defaults, use the power switch on the back of the computer to reset it by toggling it off and on 10 times with no more than 3 seconds "on" and 1 full second "off" each time.
If that doesn't work,bring it to a repair shop before you burn out the 'South Bridge' and thus needing to replace your entire motherboard (minimum $140 + labour)