The problem isn't so much the ground based computer server systems. It's whatever supplies and connects them. Should we ever get hit with a substantial enough EM Pulse, Solar Flare or Gamma Ray Burst or something we might not even be aware of yet, the satellites may be the first to go. Without those, we lose significant communications capabilities, as well as systems like GPS. Then you have the power distribution systems. I've seen it posted that major components like transformers are built on demand with no back stock. That could mean months, maybe years to rebuild after a significant system disruption. Without power and interconnecting communications systems, the web won't function very well, even if the data itself is protected.
Cell companies are moving temporary towers into Florida now ahead of Dorian. Does anybody really think they have enough to replace nearly the entire system worldwide in a catastrophic failure?