TV? Or does “no video games” imply “no moving images on a glowing box” generally?

Develop a love of knitting.

Play endless games of Solitaire with a deck of actual cards.

Write a novel.

Torment a small animal and/or child.

Or I guess you could accept the fact that being ill sucks major amounts of bum and do whatever to try and shorten it… drink plenty of fluids, rest as much as you can (even if you can’t sleep, don’t do anything active), that kind of thing.