Backup fails; Restore fails; Update fails and More; Like Groundhog Day

Here are the problems I'm trying (and failing) to fix. Not sure what the root cause is.
Windows Update fails with a message Microsoft can't explain
Windows Backup fails every night, cannot be accessed
Outlook 2010 shuts down every couple of minutes, has to be restarted
IE 11 stops and restarts every few minutes
Recovery can't restore at least 3 previous restore points, volume shadow copy times out
Windows won't shut down or restart except physically using hardware
Install Windows from DVD with updates ran for 12 hours without finishing
Install Windows from DVD without updates won't work because the installed version is newer than DVD version
Boot from DVD won't work because the keyboard is inoperable until Windows loads
Cannot change boot order, or enter into BIOS, because keyboard is inoperable until Windows loads
SFC won't run because Volume Shadow Copy fails
The last good backup is back in mid March, getting old fast
Neither MS Security Essentials or Mal Software removal tool found any malware on the machine
Desktop computer is running Windows 7 Ultimate 64bit on a quad core AMD with 12 GB of memory and 1,3 TBytes free on C: drive
I could use suggestions for a fix, thanks.

Wrong! One keyboard is a Dell the other is HP. Neither works while the system boots. I cannot use Del key to boot into bios, F8 key before Windos loads, or mouse or keyboard to load Windows safe mode. Thats why I say it's like Groundhog Day (if you saw the movie). Windows loads, programs like IE, TTax etc work but I cannot fix the problem.
Because you are the only one who even responded I must ask you for some help. The Control Panel System page says the product ID is not available nor is the Windows status. I ran the Genuine Advantage Diagnostic Tool to see what it says although I know my Windows copy is legitimate (Microsoft gave it to me). It failed to run! How can I check my product
key is intact?

Hello...
It sounds like you have a USB keyboard and that the usb ports are disabled in bios. And it's not wireless keyboards you have right?

One thing you can try it is to reset the bios. Disconnect the power from the computer and remove the cmos battery for 30 seconds and reinsert the battery. When bios has returned to default mode, the usb ports should be enabled in bios again and the keyboard should work again, so you can enter bios and access the F8 menu, and from the F8 menu you then can try to repair your windows installation