If the system has been left standing for some time without being used.
Your best option is to remove most of the parts that plug into the motherboard.
Take out any graphics cards that may be seated in the Pci-e card slot of the motherboard, and disconnect power to the card from the Psu if it requires power from it.
Remove all of the memory sticks out of the memory slots of the motherboard.
For hard drives re check that the Sata data cables are securely seated to the drive and to the sata ports of the motherboard, along with power connected to them for the drives in question.
Double check that all of the power points or connectors from the Psu are fitted to the motherboard where required.
And are firmly seated in there sockets.
Clean any dust that may of built up on the motherboard, and graphics card.
Then re insert the graphics card back into the system, making sure it is seated flush and firmly to the pci-e graphics card slot if using a Pci-e based card, then connect any extra power from the psu of the system to the card again if it requires it.
Place a memory stick in the first memory slot of the motherboard.
Look at the back of the system tower, and on the Psu it`s self make sure if it has a rocker switch on it, it is set to the right position for normal power operation.
Try the power button on the system to see if it then powers up or posts for you.
If it does turn it off then add another memory stick to the system via the memory slots of the motherboard.
Test the system again for a post and power up once done.
And repeat the process till you have all memory sticks fitted to the system.
The rocker switch on the Psu is often forgot about, and it can be a simple case of just switching it over to it`s normal power state for the system to work right.
Obviously check the power cord, and that the fuse in the plug has not blown for some reason.
As to the cause as why the system does not power up. or try another power cord if you have one.