Earlier quoted context omitted.
But the electricity powering the Internet is also somewhat oil-based, depending on exactly what fuels you local plant runs. It may not impact the individual homeowner, but the costs of the data centers and network providers will increase alongside oil prices.
Very little electricity is petroleum based anymore. Depending on region it's mostly coal, hydro, or nuke.
It depends entirely on pricing. Most "coal" plants switch between coal and natural gas based on current market trends. And even if coal is burned, the fuel to get the coal to the plant is petroleum-based.
There are a lot of complexities involved. Of course, working in the natural gas industry, I only have limited knowledge. :)