Windows 8 sometimes stuck, sometimes can't boot with 0x000000e

PC keeps crashing in weird ways. Symptoms:

1. I have a Windows 8 Box that sometimes (I suspect under heavy load) get stuck, but in a weird way - PC unresponsive, but I can (most of the times, sometimes I can't) still move the mouse and the mouse's icon changes according to the window it's in. Can't interact with the windows whatsoever.
2. Sometimes when I boot, I get a bluescreen with the error code 0x000000e (not 0xc000000e, but from internet research, seems the same). the errors description is that, a required device is needed and missing.

Internet research suggests that the Box'es SSD is failing and about to die, which correlates with the crashing when I twice tried to install a program to the SSD.

I will be trying soon to go through How to Fix Windows 7 When It Fails to Boot by Tom's hardware, but my gut feeling it's just a waste of time.

What is the cause of this and how can I fix it?

If your hard drive is failing (SSD or HDD), then it doesn't matter what you do to try to repair the OS. I have seen cases like you're describing, and your internet research is most likely correct. My recommendation is to back up everything, if it's not already too late, and replace the hard drive ASAP.

However, if you really want to be sure, you can download free hard drive testing tools to verify your drive's health. The one caveat would be the fact that SSDs can be flaky; the drive can report healthy, and still fail. That's why I don't store important files on SSDs.