The biggest problem isn't that modern computers depend on some piece of technology or process that is lost to us. It's that all the people who understand every step in that chain, from survivalist blacksmiths who can smelt ore to make tools to industrial chemists who can fashion substances that nature doesn't readily provide to electrical engineers and developers who will actually program the damn computer in year 9, are currently widely dispersed. Put them together and give them what they need and I think they could get the job done more quickly than you think.
Of course, it's more likely that everything and everyone you need will be scattered around the world when this instant occurs, and if that's the case, I'd honestly bet it would take hundreds of years to independently reinvent a modern computer because you'd need to reinvent most of modern society to gather the people and the materials to do that.
The argument is that getting from animal-powered devices to solar/nuclear/whatever powered devices while at the same time switching from 90%-agricultural workforce to anything more progressive can happen only if there is a cheap source of energy available - and we already have mined and spent all of easily available fossil fuels.
Even if all kinds of fancy devices are available and constructed by rich enthusiasts, the lack of cheap steam power ensures lack of cheap steel/etc, and all the technologies don't get the mass adoption required for their improvements, there are almost no advantages for industrialization, so the world gets stuck in feudal-agriculture systems as the local optimum.
http://opinionator.blogs.nytimes.com/2012/03/13/in-africas-v...
It wouldn't have quite the pop of surface-minable coal and oil, but if you were pushing for high technology it would boil water, drive steam engines - but maybe it wouldn't happen in England. Where you'd get the metal from is another question.