HP link. This is your computer correct?
HP Pavilion p6310y Desktop PC - HP Customer Care (United States - English)
Motherboard Link.
Motherboard Specifications, M2N78-LA (Violet6) HP Pavilion p6310y Desktop PC - HP Customer Care (United States - English)
From what you are telling us it does seem that the motherboard may be bad. However there is a few things we can try. Just leave the case open during these steps.
1. Make sure that the CPU cooler fan is working. Your computer may be simply overheating and the cpu crashes the Windows installer.
2. Remove the RAM and only place one stick back in. Make sure it is properly seated. Bad ram can cause the installation issues that you have seen. If one stick does not work try the other.
3. Disconect the CD/DVD Drive and all other items from the motherboard and the power supply. Only leave the power conectors for the motherboard and the front pannel connectors pluged in. You power supply may be going bad.
4. Clear CMOS. Make sure to unplug the computer before doing this. Go to the motherboard link and scroll down near the bottom of the page. Now we know that the computer is in a basic state and now everyone knows where you are at with the system.
5. Start the computer and let it run for about 20 min with nothing connected. If it does not crash then we can move forward.
6. Now connect a mecanical drive to the motherboard and power to the hard drive and turn on the computer. Go into the BIOS and see if it appears. Do this for each sata port. This means turning it off to change ports. If it shows up in each port then we can move forward.
7. Now using connect the CD/DVD Drive to your computer and try installing windows using the DVD. NOT THE FLASH DRIVE. If it installs then we can move forward.
8. Now using the flash drive reinstall windows over the new installation. This will allow us to see if part of the motherboard is bad. IE the usb controler.
9. If you are at this point and the computer is working then I am not sure what went wrong.
Post on how far you got with what I have posted. I have a few things to do tonight but I should be back on by 11:00 PM eastern.