I have an AMD 9750, GIGABYTE GA-M750SLI-DS4 AM2+/AM2 NVIDIA nForce 750a SLI ATX AMD Motherboard, Radeon 4870 and Western Digital SATA 640 gig hard drive with a SATA DVD RW. I can get the files of my Windows Vista 64 bit to start loading but once it starts to install the computer reboots. Any ideas? This is a fresh install on a brand new hard drive.

Do you have two sticks of Ram? Try removing one stick and attempt install with one stick only. Let me know what happens.

I have only installed Vista a few times so I can't really remember the process.  I know XPs install and after the files are copied over the system reboots then prompts to boot from cd.  You just ignore that and let it boot to the harddrive or you press F12 and select boot from harddrive.  The the install will continue.

What is your power supply?

This has been covered before in other posts, but try installing from a IDE optical drive instead of a SATA one. Most Nvidia chipsets have issues with SATA optical drives and will blue screen and reboot during OS installs.
 
If this solves your issue, you will not be able to re-install the SATA drive as your system will still BSOD during bootup of Vista or XP.