Remove the hard drive, mount it in a 2.5" external USB shell and connect it to a working system.  Copy what you need.

Before proceeding with the reinstall, run an extended -- not just quick - hard drive test.  F12 at powerup.

I ran the extended scan in the diagnostics under f12. It said there was no errors. I'm not sure I will be able to take the hard drive out as I have a laptop. I'm also afraid of messing it up since Ive never taken one out before.

If you have an external drive, you can also make a bootable Linux flash drive, boot the system from it and use that to copy what you need to the external drive.  If not, contact a local computer repair shop for assistance.

Would it help if I created a Windows installation drive using the Media create tool and repair the BCD file that way? I've seen some videos on how to do it. They are all similar and I think I can do it that way.

It depends on what's wrong.  And I would not make ANY attempt at recovery before you've made a full backup of any files you can't afford to lose.  Chances are that now, you can recover your data -- if you make an attempt that fails, you may lose that option.

Get the data off the drive before proceeding.

I was able to create an installation USB. After loading up and selecting repair this computer, I ran the diagnostic tool. It started to run, then restarted. I'm not even sure it fixed anything. It still won't boot. Now when I try to use the USB again to access the command prompt, it is giving me another blue screen with the error code 0xc000000e

I ran the diagnostic in the f12 menu and instead of the partition table having an X by it, the boot files have the X. Did something break the USB? I originally had either Windows 7 or 8 and updated to 10. The installation file is for Windows 10.

maybe, you can choose to backup files in safe mode( https://www.backup-utility.com/backup-restore/backup-files-safe-mode-4348.html ) before you reset your computer.

That link doesn't work. I can't even get into safe mode because the computer won't boot up enough to even get to safe mode. I can't boot windows at all to be able to boot to windows.

What model system do you have (i.e., XPS 9550, Inspiron N5110, etc.)?  And is it a hard drive, or a solid state drive?

Please try the following fix and see if that helps you:

www.kapilarya.com/fix-the-boot-configuration-data-file-is-missing-some-required-information

Now, something that was not detailed in that link, so here are the steps to be executed::

1. If you don’t have a restore media or system disk to perform a recovery download Windows 10 from:

www.microsoft.com/.../windows10

This will only download a simple tool which you can use later to create a USB or DVD image with Windows 10 which you can use later to perform the recovery.

2. Restart PC with the USB/DVD, selected advanced recovery options and then open administrative Command Prompt.

3. All you need to do is enter following command :

    bcdboot c:\windows

Substitute C with your system root drive letter in the above mentioned command. This command allows to copy BCDboot file from existing Windows partition to motherboard partition and creates the BCD store in the same partition. 

Hope this helps.