This brings to mind something David Mitchell said once on Would I Lie To You (British panel show):
In response to Kelvin MacKenzie's claim that the "This Is My" guest had built him a nuclear bunker:
David Mitchell: If there's a nuclear war, I don't want to live. I don't want to come out of a shelter and try to rebuild society. I have no skills. Okay, society is destroyed by a nuclear war, we're basically - we're back to the bronze age...how long is it gonna be before people start pitching panel shows again? It's gonna be at least 2000 years!
Watch it here if you want, it was annoyingly hard to find.
However I don't think David - who is a comedian - is precisely right about how such a war would affect the state of technology. If there are survivors, I don't think we'd really be back to the bronze age. Even if all technology was destroyed (which it wouldn't be), give humans a few decades, we'll have some sort of modern technology back up and running. Maybe not computers, but some certainly some analogue electronics - the knowledge isn't lost. Communications would be one of the first points of focus, so television would follow closely behind.
Yeah, chip fabs are exactly why I think computers would need more time. I'm not super familiar with this, but I'd wager such a factory can only be built using tools and machines that come from other specialized factories, and so on maybe 3 levels down before you get to a relatively rudimentary manufacturing process that can be reasonably achieved within a few years. It would take a lot to get that back up and running.