Sorry, I'm confused.
The recovery partition from Tech Tool, this is on the internal HD or on a CD/DVD?
Is this the same thing as the TechTool disk that your computer can boot into?
Where is the Disk Utility that cannot see your hard drive? Is it on the Apple recovery partition on your internal drive? Are you saying that Disk Utility on your Apple recovery partition cannot see your boot partition?
It sounds like your internal boot partition won't work, but the internal drive itself is OK (i.e., Disk Utility, on your Apple recovery partition, doesn't see the normal boot partition), or at least OK to the extent that the Apple Recovery partition can run.
If you install Mountain Lion on your external drive and use it as the boot drive for your computer, it will be very slow, and you won't be happy. I'd forget that idea.
Assuming I am thinking correctly about your situation, I would try to repair your HD. Your options would be:
- a safe boot Mac OS X: What is Safe Boot, Safe Mode? and then disk utility
- boot into single user mode and see if you can repair your hard drive Repair Your Hard Disk in Single User Mode | Everything Macintosh
- internet recovery OS X: About OS X Recovery
- recovery disk assisant, if you have made one already OS X Recovery Disk Assistant v1.0
If none of that works, then I'd try and wipe the entire drive and start over. I'd try to do that from internet recovery. Hopefully one of your external drives has backups on it.
If that doesn't work, then I'd replace the drive.