Sounds as if fans etc might be struggling because clogged up with fluff.
With pc unplugged from mains electric, take side off and clean out any dirt and fluff using a paintbrush and the nozzle of a vacuum cleaner held near - don't let nozzle touch any of the pc inards or you might damage them. Next make sure all the components (ram sticks and any cards) are firmly plugged into the motherboard and all cables to harddrives etc.
Leave side off pc and plug back in mains and boot up. Look carefully at the fans - don't touch or you'll lose your finger end - make sure all are running smoothly.
Post back and tell us if the pc now boots up okay or if it doesn't tell us what if anything is displayed on the monitor.