Well it is good you have a backup. Is this computer considered the actual server. Do you back up all of your computers. It just sounds like you did not have a good backup.
You want an external drive, hopefully 3.0 or SATA. You want to use a 3rd party software even though Microsoft's native one is decent. But, I don't think you can do a bare metal backup with it.
There are many like OO and Macrium, etc. I use Macrium on my clients and server along with BackupAssist. But, Macrium makes it easy to do bare metal backup with the ability to image or clone. Plus, you can restore to dissimilar hardware. The idea of the bare metal backup is so you can restore no matter what the drive is doing. You should not have to use a repair disk. Most backup programs recommend you make a boot disk for their actual program. One nice thing about Macrium is it will download and install WinPE (a pre-environment) so you can restore from from the BIOS during bootup.
Have you booted into safe mode and uninstalled the update?
Have you put this on EE? Don't worry, no one does, lol. It's just free during the trial and there are only 30,000 experts better than all of us except Sandeep.
Purchasing a new OS is no big deal. Just go to Staples or download a cheaper one. Get an .iso image and burn it to a DVD. If you want to fix it, just pay the money.
Finally, have you thought of Microsoft Support? They are a bit pricey, but they will likely fix the problem if it is software related. After all, it may be their update that did it. Again, they can be pricey, but they will charge you up front, but they generally won't charge you if they can't fix it. And, there is no better support. They are incredible once they log in. If they can log in. But, there are ways to do it even if you can't boot into Windows.
Have you tried moving the hard drive to a different computer and see if you can see it? Can you boot to it?
Good luck.