Launcher won't sign in to Minecraft accounts

I have been experiencing this issue for about 4 weeks and have taken as much action within my power to fix it myself.

The issue is that when I try to sign into the Minecraft Launcher, it shows the error "Sorry! Make sure you are online and try again", even though I am clearly online. I have tried going to friend's houses and try to connect there, and that didn't seem to work either.

I have contacted the Minecraft Community Support team and they have concluded that it is not a PC issue, and advised to contact the bug tracker team.

Marked as private as the screenshot attached may contain personal information.