Hi Evan. I'm Greg, an installation specialist and 9 year Windows MVP here to help you.
Run Disk Check here https://www.groovypost.com/howto/check-hard-dri... from the Command Prompt in Repair mode, accessed by one of these methods: https://www.tenforums.com/tutorials/2294-advanc...
If it fails then Test the hard drive with diagnostics: https://www.lifewire.com/free-hard-drive-testin.... Best is Seatools bootable Long Test which works on all models:
http://blog.nowherelan.com/2013/04/04/boot-seat....
https://www.seagate.com/manuals/software/seatoo...
If the drive is failing, I'd replace it with an SSD which is the best Upgrade one can have - lightning fast, faster than a new higher-end PC without one, especially if you do the gold standard Clean Install in this link which compiles the best possible install which will stay that way as long as you stick with the tools and methods given, has zero reported problems, and is better than any amount of money could buy: http://answers.microsoft.com/en-us/windows/wiki...
If the drive is OK then you'll need to get Disk Check to run so that it fixes the file system. It may be necessary to create bootable media to access Repair Mode or do the Clean install since it relies on it's own files and drivers and not those onboard WIndows that may already be corrupted.
To create Windows 10 Installation Media on another PC install Media Creation Tool and follow the directions here: http://windows.microsoft.com/en-us/windows-10/m.... Uncheck the box for Recommended Settings to choose the exact version and bit rate for the target PC only.
Insert media, boot it by powering up PC while pressing the BIOS Boot Menu Key: https://www.sysnative.com/forums/hardware-tutor...
If the media won't boot you may need to enter BIOS/UEFI Setup (pressing key given in chart in link above) to turn off Fast Boot or Fast Startup first.
Choose the boot device as a UEFI device if offered, on second screen choose Repair Your Computer, then Advanced Troubleshoot Options, then Command Prompt to run Disk Check.
If you need to rescue your files you can try this method: http://answers.microsoft.com/en-us/windows/wiki...
I hope this helps. Feel free to ask back any questions and let us know how it goes. I will keep working with you until it's resolved.
______________________________________________
Standard Disclaimer: There are links to non-Microsoft websites. The pages appear to be providing accurate, safe information. Watch out for ads on the sites that may advertise products frequently classified as a PUP (Potentially Unwanted Products). Thoroughly research any product advertised on the sites before you decide to download and install it.