Hello and thank you for choosing JustAnswer.com
My name is ***** ***** the expert helping you today with your Lenovo Flex Ideapad.
First.....if you have RUN OUT OF SPACE (thats why you have 0 bytes free) you should DELETE progrmas of files you dont use or need anymore to free up some space.
Secondly, you can add a SD card for extra space, so instead of DELETING the files, you could MOVE them to an SD card connected to the Lenovo.
I think you dont believe the Best Buys advice, and that is normal, and frankly i dont EVER refer people to BEst Buy geek squad.....they are really bad, customer service is crap....but that is a whole other story.
Running out of space shoudl NOT keep the internet from working.......but it can cause all kinds of UNKNOWN issues.......but its NOT SUPPOSED to.
So you may have OTHER issues than just running our of space.
I would suggest a remote session.....but you say the internet wont work??