"I read somewhere on the internet" that all the designs, blueprints, specs, and whatnot for the Saturn V were essentially lost since they were not collectively archived by the multitude of subcontractors and hence scattered to the metaphorical winds. I could, as they say, be wrong............
Paul Shawcross, an agent with the NASA Office of Inspector General, says:
...the Saturn V blueprints are held at the Marshall Space Flight Center on microfilm. The Federal Archives in East Point, Georgia, also has 2,900 cubic feet of Saturn documents. Rocketdyne has in its archives dozens of volumes from its Knowledge Retention Program. This effort was initiated in the late '60s to document every facet of F-1 and J-2 engine production to assist in any future restart.
I'm sure this isn't enough to build another moon rocket. And I'm sure there's a lot of material that was either 1. not recorded or 2. recorded but now lost to the ages, both on NASA's part and the plethora of sub-contractors. But I cannot conceive that it is physically impossible to make a Saturn V today (financial issues aside).
There's also new regulations, laws etc that may come into play. Some of the materials & systems used in the '60s may be outright banned today due to toxicity or environmental issues. Those, obviously, could not be legally reproduced. But that doesn't mean the technology or manpower to do so doesn't.
Bear in mind, you need more than just the rocket. You'll need to refit the VAB (which was converted to stand the shuttles up & mate with it's booster rockets and external fuel tanks), refit the Crawler (again, because of the shuttle), and a launch pad (all the Apollo pads are now gone, or stripped and the concrete is (abandoned in place'). Mission control has also been completely remodeled to accomodate the ISS. So the Saturn 5 is just part of the job.
You'd also have to recreate things like tracking stations, radio com systems, telemetry stations, contact the US Navy for capsule recovery, ad nauseum, ad infinitum.......