Insider Fast Track Office
Hi have you tried this before.
where the arrow shows on your screen have you left clicked your touch pad, as that may bring up your log in screen.
Also have you clicked on the red x for the internet, as that should bring up several networks, find yours and see if you can click to reconnect your network.
Why I am asking is because my friend had the same trouble on his laptop, and that is what I did to get it up and working again for him.
Let us know how you get on
If none of that works then, do use another computer, the one you have written about will do.
Also when you pressed F8 did you press FN at the same time, also F8 Safe mode on windows 10 does not believe work.