My computer's over five years old and it can run Skyrim. The great thing about Bethesda games is that you can more or less reduce them to nothing for most computers to play them. I think you need 2.0 Gtz duel core processor, memory of 2G and space on the hard drive of 5-8 Gb.
My computer is geared out to work with 3D animation, so that might be why I'm able to play modern games on it...
Oddly enough Skyrim actually works better on my PC than Fallout 3.
Trust me, the initial cost of PC gaming is outweighed by how cheap you can get PC games. We're talking games that launch for 60 dollars, but on PC, give time or a sale, can drop down to 15 dollars. Amazon, GOG.com, and Steam are usually the best for that sort of thing. You can literally get box copies of PC games on Amazon for around 2-20 bucks that are only 1.5-2 years old.
PC Skyrim plays like a clumsy port of the console version, just saying.
Also the whole draw of the game is the fact that the world looks awesome. If you got the money and an HD TV, I'd say it's more worth it to throw down for a console where everything will definitely look amazing than get a crappy PC with a tiny screen where everything is low res and laggy.
It would depend on a lot of factors. I would bet you could get it to run on a fast P4
The better question is how much you want to spend, and why you don't just buy a 360/ps3 if you want cheap gaming? A console would actually get you higher quality per dollar (up to a point) and in your case it seems like a much better choice overall, budget depending of course.
What would be considered a fast p4? Systems specs on my comp inform me that I currently have a 3.00 GHz.
As for why I don't just buy a 360/ps3, it's because, to me at least, it seems far too late in the console race to spend the money. Heck, there's already a fair bit of talk about the playstation 4 from what I've been reading, albeit just rumors.