At the end of the installation procedure of 64 bit Ubuntu 12.04 on a reformatted partition, I got a grub2 fatal error 10. I rebooted and the grub2 command prompt read, "error: unknown filesystem." How can it not know the file system? I chose btrfs. So I boot the live-USB and search around on Google and stumble upon boot-repair, which ostensibly seemed like a useful utility. I install the app and then run it. I click the recommended repair option. At the end of the process, it gave me this link to share for further troubleshooting purposes: http://paste.ubuntu.com/950561/
Upon rebooting my PC, all I get is the Windows loader. There is no trace of grub2. I write this forum thread from Windows 7.

What has gone wrong and how do I get 12.04 running? What other information could I provide?

The first paragraph of the bootinfoscript tells you

You don't have an sdb7 partition. You show an sda7 partition with btrfs but no boot files? Do you still have Slackware, Gentoo and xp installed along with windows 7? You don't seem to have any Grub2 files except for those on sdc which are your CD or flash drive.

I don't know which boot-repair utility you are referring to but, apparently it just reinstalled windows 7 bootloader to the mbr.
How were you booting previously if you had the other OSs' installed? Grub Legacy? Lilo? Which was the primary bootloader prior to trying to install Ubuntu?