Can't successfully install Mavericks or Yosemite to MacBook Air

Let me tell you my story of OSX and woe.

I've been trying to fix my wife's 2013 MacBook Air, with 1.3ghz processor and 4gb of RAM, all stock, no upgrades or peripherals, running the latest version of Mavericks. The proglem began with some difficulty from waking up - you'd open the lid and the screen would remain black. Sometimes waiting a while would work, or opening and closing the lid a few times. When it didn't work, there was nothing to do but hard reset it (hold down the power button).

I attempted to reinstall Mavericks over the old installation using the recovery partition. Everything seemed to go well until it rebooted, at which point it got stuck on the Apple Logo with the little spinning wheely bob below. I left it overnight, but it never got past that point.

I zapped the PRAM and reset the SMC (I believe this worked, although there appears to be no indication if it does). I tried a new installation of Mavericks, same results.

At this point I used the recovery partition to wipe the drive and install a fresh copy of Mavericks. I wiped the drive in recovery mode and for good measure, I fixed permissions and repaired the drive. I also restarted in single user mode and tried to repair the disk using fsck. New installation cruised along until reboot, at which point it got stuck on the Apple Logo again.

I tried creating a USB installer for Yosemite and was able to boot from it, but it would just display a black screen with the Apple logo and a progress bar, but would never proceed past 50%.

At this point, I was able to boot the computer into safe mode (using the existing Mavericks install) and set up her user account. I downloaded and installed all updates and restarted, but on normal restart it got stuck at the Apple Logo again. Nothing else was installed, and I had no login items or peripherals plugged in.

I attempted to upgrade to Yosemite using the App store while in safe mode. It downloaded and I ran the installer, and upon rebooting, the loader (black screen with Apple logo) gets stuck about halfway, just like before. I let it run overnight, but it never gets passed the halfway mark. Furthermore, I can no longer boot into safe mode or the recovery partition. Weirdly, about 15 minutes in to the installation, a voice comes over the speaker and says "If you'd like to continue in English, press the return key," but still only displays the loader progress bar. The voice lied, hitting the return key has no effect.

I'm out of ideas here, but wanted to post to the forums before I go into the genius bar. Has anyone experienced something like this before?