Can static electricity buildup in house wiring prevent you from connecting to the Internet?
Static electricity can only affect a connection if it was discharged and damaged one or more components needed for that connection. RFI (Radio Frequency Interference) is much more detrimental to a connection. It sounds like you may have gotten the two confused. Wires (even from electrical fences) can cause a lot of RFI, but can oftenly be confused with Static Electricity as the cause.
No. Static electricity does not build up in wiring. Even the presecence of a strong static or DC voltage outside the wire should not affect the connection. High frequency electrical fields near the phone wire or cable (as the case may be), such as might be caused by the wire running too close to a flourescent fixture, might cause problems.