You might be able to do it for $400 - $500 depending on what exactly you have already that could be reused for a bit.
ie. You say your current system is a P4 -- what are the rest of the Specs - Mainly Case, Mouse, Keyboard, HDD, DVD drive, PSU, - Is the Windows system on it a Retail or OEM license (that alone is around $100 of the cost if you need a new OS) -- Also what monitor do you have and do you plan on changing it ? (what GPU is needed will be influenced by the resolution you plan to play the games at !)
For something that can play Witcher games and Skyrim etc. you don't need top shelf components if you are willing to compromise on the settings a bit until you can save up some more $ and upgrade the system so you can then upgrade the settings in game !)
LEt us know what you currently have and then we can see what is needed immediately and what can wait awhile and still let you play at decent levels until then.
I'm not sure if you understand how outdated my computer is, lol.
I'll keep the monitor, keyboard, and I don't care about mouse, I wasn't including that - we have working mice around here.
My monitor is old, but that's something I can always replace later. Its max res is only 1280x1024. I think I paid like $20 for it or less.
The graphics card is the other thing I thought I could pop in. It's my brother's old one, and not top of the line, but it would at least let me browse the internet/play older games: Radeon HD 4670.
I just figure I can pop it in to get it started, get my data transferred and all that - my current PC literally feels like it is on its last legs. It beeps on every startup (press F2 to continue) and blue screens on every shutdown. It's crazy. I'm going to see if I can fix it a bit until my new computer gets here. (I'll be able to buy the new computer or the parts to make it within 1-2 weeks).
My OS is currently XP. For the new one, I 100% plan on getting Windows 7, which I realize unfortunately costs a lot. AAAAAAAAAAAARGH
As to whoever said to use my current HDD - it's 140 gigs, and has the Windows XP I mentioned on it. I'm not sure if the problems coming from my PC are because of it or because of hardware or what.
Also. I definitely want a new case. This one is basically a school/office looking IBM. The only way I got my graphics card in was to get a low-profile card. I can use my old DVD drive, though. It's fine.