Client Won't Patch on Windows 10

I've recently installed League on a new computer that uses Windows 10. When I get to the part to patch, however, it downloads to 1652 MB and then completely stops downloading.

It is not my internet/wifi connection. I've checked that.

I've also tried uninstalling and reinstalling.

I've tried to run as administrator.

I've changed compatibility to Windows XP (service pack 3) as well as Windows 8.

Short of reverting to Windows 8 (which is not an option) or running it on a VM, I'm at a bit of a loss as to what to do next.

Help please? ];