What you need is to work on one alternative reality or counter-history
If you want internet working strongly and steadily after the apocalypse, then you'll need to move all the internet infrastructure to space, then, you need something that damages almost all the electronics on earth but leave satellites mostly untouched and satellite servers storing websites & stuff untouched, so, to say, all the internet was moved up to be fully satellite communication, nothing ever exist on earth physically of it after and after that, in some point of history the cataclysm happened, but for that moment the internet was already safe there.
Then is the electricity stuff, if you want to make something like electricity still exist, you can make something like kinetic generators or somewhat improvised and modified water generators/windmills, using brute animal force is a way to go too... but you must say than the power is keeped in some batteries or something, we don't have the same demand than today now, because just the 2% of the population survive.
But then again, how will you have the knowledge to do that?
Well there are two choices here who are both compatible between them two...
1) The survivors are mostly returning from somewhere/something from where they survive the effects of the plague, when they return they'll be vaccinated from the virus by the few survivors who made it.
so that way you can justify have a bunch of experts to rebuild something like a safe perimeter, like a safe-city or something who actually have internet and generates enough power to itself but without saving themselves from the apocalypse.
2) The survivors find and study the Safebox of knowledge kept to restore civilization, that thing actually exist, so they learn the knowledge to make them own safe haven and you take them from there.
What can make that apocalypse happen?
Zombies? Human-Bots Wars? But bots are controlled by a super-computer and using biological weapons, or something like that?
In fact a Big Brother computer use the virus to attack humanity, but the mutants just go too fast out of control.. so the mutants harrass humanity but also the big brother computer, leaving humanity and that computer almost utterly destroyed (or just utterly destroyed saving some humans).
That should explain your problems.