What you're looking for is some way to load the CHKDSK Error reporter type thing Windows has. Since you can't access the desktop/ boot up fully you're looking for a way to boot it up in BIOS or any other System application you have built in to your PC which is definitely impossible (There are some built in applications that allow you to access files on a USB or Hard Drive) even then it's not a guarantee fix.
Oh, I almost forgot to mention, there are also a few troubleshoot options when you press F8 and Select Repair your computer, the troubleshoots it comes with don't usually fix anything but I guess it's worth a shot.
Your safest option though is to definitely do a full system restore, you can download Windows 7 or Windows 8 on a website and convert it into an iso.
You can buy a code on their website or if your PC came with a Windows code.
Like Faint said, as long as you didn't customize or open up the case of your PC/ Laptop you should still have your warranty.
Full system restores are a good thing for your PC, it can sometimes increase boot times and you should still have a folder called Windows.old so you can access your old files.
To faint