
Once you have a bootable thumb drive, you can boot from that drive using the same Option-key startup, and then selecting the thumb drive (give the drive a unique name, so it's easy to recognize). You can then boot into the Recovery partition using the method you've used before, format the thumb drive using the steps outlined below, then install Mavericks on the thumb drive using the installer in the Utilities menu. The thumb drive should be at least 16GB bigger is better. If you've got a USB thumb drive, you can install a full copy of Mavericks on it. You'll need an external drive to boot from, with an operating system late enough to start your computer and a copy of Disk Utility on it. There are commercial utilities such as Disk Warrior and Drive Genius which can do directory repair while leaving the data more or less intact, but let's review the brute-force method. Fortunately, when you format a drive, it constructs a new directory if you then copy data off a drive with a damaged directory, the new directory is filled in with the relevant data as the copying operation progresses. Normally, the technique for replacing a damaged directory is to reformat the drive, but that erases all the data that's already there.

The likely cause is catalog/directory damage, not a damaged OS.

You have two different Apple applications (Finder and Disk Utility) reporting two different data amounts. I don't think she saved anything via Time Machine in the past year.

How do I navigate to these folders and delete them? Any other thoughts, guys, on what else to try? I'm thinking the OS may be corrupt and I may have to reinstall it. My daughter says I can erase her Blockrock Shooter and Accel folders. I can get to Terminal, but I don't know how to navigate. I've run the Fix Disk and Repair Permissions thing but didn't remedy the problem. It says I still have 148GB free of the total 250 GB capacity. Pressing the option key at boot up, I can choose Recovery Mode and use Disk Utilities.

And I don't get to the point where I can see the desktop. Shortly, the cursor arrow (which moves as I slide my finger over the trackpad, but can't do anything else) appears at the left upper corner of the screen. After a few moments, this message disappears and I get a blank white screen. After a few seconds these disappear, and a message pops up saying that the Hard Drive is full and that I need to erase some files to make more room. When it is turned on, I see the usual Apple logo and spinning wheel at the bottom. My daughter uses this Mac Air (2011, Solid State Hard drive), which is upgraded to 10.9 OS.
