So some of you might have seen my frantic 2 am post about my Macbook Pro refusing to boot.
TL;DR: I was pretty sure I needed to reformat my hard drive, but I didn't have a backup of my computer because apparently I like to live on the edge. Cue panic.
Friday evening we spent two hours dealing with the Apple Store to be told what I already knew: there was no way to get my data off the computer without fixing whatever was corrupted on my hard drive, which would erase all my data. The only option seemed to be a data recovery tool that might be able to repair the disk so it could boot again. That was going to cost a lot of money, and even though FatherToad offered to pay for it, it was not something I wanted to do. I was pretty bummed out.
And then!! MrToad found a way to solve the problem, as usual. It's actually a pretty cool fix so I'll lay it out here. He downloaded Ubuntu on a 16gb flash drive, then, since the Apple Store people said everything else was fine, he was able to boot Ubuntu as the OS on my Macbook. From there, I could access all the files on my hard drive. He had to do some code-looking stuff in order to be able to have permission to move the files, but he did it and we were able to move my important stuff onto an external drive, erase the disk, and reinstall Yosemite no problem!
Bonus: I got really self-conscious before going to the Apple Store and cleaned my computer obsessively, so basically it's like I have a whole new computer.
Thank you so much to everyone who offered help and explanations!!