I run a dual-boot setup similar to yours with
W10 and Linux (Ubuntu 14.04LTS) on my Acer AspireOne netbook (c.2010), and I've had to re-do it a couple of times to get it to work properly.
One of the keys to doing this is that you may have to wipe your hard drive with a Linux tool rather than relying on Windows tools. You can use either the manufacturer drive-wipe program for your particular drive which you can download for free from the manufacturer's website page. For example, if you have a Seagate hard drive, you'll need to get
SEATOOLS from their website or if WD, you'll need
DLG. Here's a complete listing to cover whatever make of hard drive you have:
Hard Drive Diagnostic Procedure You can also use the excellent
GParted, included on the Ultimate BootCD (UBCD) compiled by Benjamin Burrows in ISOLinux. Here's the link:
www.ubcd.com. You can download it for free and install on a DVD or USB stick and even distribute it for free as long as you don't charge any money. It's part of the GNU public domain license. I suggest you reformat the bootdrive with NTFS format if you use
GParted to do so, it worked great for me.
If neither of these works, and you can't get rid of the multiple W10 installs, you'll probably have to use
DBAN, which is also included on the UBCD disc or usb stick. The included version is not the top of the line DoD erasure method, but it will do the trick for commercial products like windows and Linux. I will also mention, that I didn't need to
DBAN wipe my Acer netbook drive to be able to reinstall W10-Ubuntu dual-boot. But some computers, and some hard drives are stickier than others so I'm including this option in my discussion as a last resort.
If none of these works, there is a high likelihood that your hard drive may be failing or have failed. You need to run both the short and long tests in the appropriate flavor of the diagnostic for your make hard drive such as
SEATOOLS for a Seagate drive, etc. If the diagnostic (e.g.:
SEATOOLS) returns any errors on either or both tests, your hard drive has failed and must be replaced!

It won't be suitable for use as a single-boot or a dual-boot OS.
Keep in mind that W10 and Linux write some tricky code in Track0 of modern computer bootdrives, especially in the first 512 sectors and it sometimes takes brute force to remove it.

Once done, and the drive is reformatted to either a
RAW or
NTFS format, you can usually put which OS back on there you want; Windows, Linux, or whatever.
Hope that helps!
Let us know how it turns out.
<<<BIGBEARJEDI>>>