Q: Can't find Macintosh HD during restore

There I was, planning my lessons for tomorrow's classes, when my computer froze. I couldn't force quit anything, so I just shut down manually. When I restarted, there was a folder with a question mark on it. Hoping it would lead me to some sort of mystery-based adventure, I clicked on it but to no avail. It just sat there like a dried turd on a Parisian sidewalk. Again, I manually shut down and restarted holding "Option". This allowed me to connect to the internet and get as far as "OS X Utilities", which asserted four options: 1) restore from time machine (yes, please!), 2) reinstall os x, 3) get help online, 4) disk utility. I started with "disk utility" but, alas, my only options were "33KB SandForce", "disk 1", and below that "Mac OS X Base System". This lead me to the logical question: had my Macintosh HD left me? No note? No goodbye? I thought long and hard about what I had done to drive my HD away, but nothing had changed of late (maybe that was the problem; maybe I should have tried harder to spice it up a bit). Then I went to "Restore from Time Machine". I've always liked time travel, but this time I felt like Marty McFly when he flips the switch in the DeLorean and nothing happens. My external hard drive was listed. I selected it. I even chose the Backup I wanted: a robust "September 28, 2014". But then a window audaciously asked me to "Select a Destination". I would have been happy to select a destination: I hear the Keys are nice this time of year, or even Prague for a change of pace. But no. It just sat there mocking me with it's "searching for disks" lodged in the middle of the screen.

And so I beg of you dear more-savvy-than-I readers, please help me get my HD back. I can change. I'll do anything. Anything.

Thanks.