I have downloaded a lot of Linux distros [both 64 and 32 bit], but I seem to have a problem when it comes to installing a 64 bit distro on my desktop gaming computer. My Samsung series 3 laptop [4 core amd cpu] has no problem installing a 64 bit distro, but when it comes to my gaming computer it is another matter.
When I run the install disc everything is fine up until it starts to ask me questions to start the install. The OS does not recognize my mouse and my keyboard, and it hangs there, which doesn't allow me to continue with the install. When I install any 32 bit Linux distro I don't have any problems what so ever. What gives???

My desktop gaming computer [which I built from scratch] has the following hardware:
AMD FX-8320 8 core
Gigabyte MB GA-990FXA-UD3
16 Gb Gaming Ram
Zotac GTX 660 video Card

Can anyone give me an idea as to why I can't install any of the 64 bit distros on my gaming computer but can install a 32 bit?

And right there is your repeatable event to begin troubleshooting.

At this point, your question should be "why doesn't it recognize my mouse and keyboard?" rather than "why doesn't 64-bit work?" First off, I'd try a different mouse and keyboard. Borrow some from a friend if you don't have them yourself. If your system supports PS/2 periphereals, so much the better. Try PS/2 rather than USB (which is what I assume you are currently using). If you are using wireless periphereals, switch to wired ones. This is how you should begin to diagnose what is going on.

Once you get it to recognize your mouse/keyboard that might uncover additional details about the apparent 64-bit vs. 32-bit difference. My guess is that it's not really 64-bit vs. 32-bit per se, that's just a symptom and not the cause. My guess is it's something else that you just haven't been able to isolate yet. Maybe something that causes one installer (the one for 64-bit) to choke whereas the other installer (the one for 32-bit) flies right over things.

Have done what you have suggested but still have the same problem. Both the mouse and the keyboard are wired to the usb 2.0 socket.

Try if you have an option to boot the machine in legacy mode instead of UEFI mode. If I remember correctly booting a 32 bit OS will automatically disable UEFI mode, so it might be that this is an UEFI issue.

No change, still the same.

Which particular distros are you trying? What are the names of the ISOs?

Look in the BIOS options for USB keyboard and mouse support.

2 things to try, both in your BIOS.

1- Enable 'IOMMU Controller'
2- Enable 'Legacy USB'

I beleive that enabling IOMMU Controller is the most likely fix.

http://ubuntuforums.org/showthread.php?t=2114055

I have checked the bios for those two items you have suggested, and they are both in the enabled setting.