Cannot Run Firefox and "Delayed Write Failed"

I'm helping a friend fix their computer (running slow, some applications not working, etc.), and ran across two things that I haven't seen before. I think they may be related, so that's why I'm posting them together.

First, I am unable to run Firefox. I have uninstalled it and re-installed it, but to no avail. I get this error message upon each attempt to run it: The application failed to initialize properly (0xc0000006). Click on OK to terminate the application.

Second, frequently this a message to this effect pops up saying something about "Delayed Write Failed". I turned off "Write caching" on the HDD per here and still get the message whenever I install an application.

Does anyone have any advice for this? I ran Malwarebytes and it didn't turn up anything. I also have run CCleaner (minus the registry cleaner) and turned off a bunch of startup programss (Firefox wasn't working before I did any of that).

Thanks.

EDIT: Here is the exact message I get when I try to install something (note: Spybot will still run):

Windows was unable to save all the data for the file {Filenamehere - e.g. C:\Program Files\Spybot - Search & Destroy\Plugins\Fennel.dll} The data has been lost. This error may be caused by a failure of your of our computer hardware of network connection. Please try to save this file elsewhere.

This is usually caused by a hardware failure of the hard drive. I experienced this problem when using a faulty SATA cable. Check the SATA cable connections. The drive itself might also be failing.