Get a linux distro from internet and make a bootable USB from it, Ubuntu or Linux Mint. Now boot the Computer from the Live USB and use the comupter to Browse internet and see videos, basically use it for a couple of days without installing the OS and just running from the USB drive.
If the computer runs fine in this experiment it will verify the following.
Your CPU is working Fine.
Your Motherboard is Working Fine.
Your PowerSupply is Working Fine.
Your DVD/ Optical Drive is working fine. (Test it using a DVD disc)
Your USB ports are working fine.
basically i mean to say test all your components (expcept the GPU, leave that for now it requires getting in and dirty) with Linux, if they work you can be at peace of mind that your hardware is working correctly and you need not go crazy swapping in and swapping out the components ok.
Don't panic, we will fix this issue you will get your pc back. It is an interesting problem. Try this and Be In touch here on therad everything will be well.
Use someone else's computer to download Linux and make the Bootable USB, I would recommend Linux Mint and using LiLi USB creator for Linux to prepare the things
1. Linux Live (LiLi) USB Creator :
http://goo.gl/YXKB
2. Linux Mint Download :
http://goo.gl/azR2 . Get the version with all the applications preinstalled , then you can do extensive computer work from Live USB without installing anything and that is exactly what we want to do for the experiment.
Don't worry, Bros are here to help.