Okay, so my girlfriend got a copy of Skyrim for her PC. She'd like it to be on the highest quality, but the framerate is terrible, even on the lowest quality it is unplayable. Here's the info of the graphics card and whatnot.

Graphics card: ATI Radeon HD 4200 (with d3d9.dll in the skyrim folder from the performance download from skyrimnexus, NVIDIA Geforce 8800 GS is the new driver for Skyrim)
Processor: AMD Athlon? II X2 240 Processor 2.80 GHz
Installed memory (RAM): 5.00 GB (4.74 GB usable)
System type: 64-bit Operating System

dxdiag:
Version: DirectX 11
System Model AY626AA-ABA p6314f

I don't know much about computers and drivers and all that, so if I am lacking any information for a possible solution, let me know. I've tried the CFF explorer and performance mod and changing the number on SkyrimPrefs, but nothing has worked thus far. Please help!

The onboard video chips are not adequate. The minimum is a real video card made by a real 3D graphics card company, Although Bethesda made the foolish mistake of writing the requirements around the least important of specifications, so that the video card part is therefore meaningless, the facts are that the minimum cards to consider are the Radeon HD 4670, 512 MBs, and the Geforce GT 240, 512 MBs (or the equivalent performance level, older or newer).

An HD 4200 is a very slow, zero-RAM chipset video solution.

P. S. One of the same message is all you are allowed to create. Duplicates are not acceptable. ( I suppose that I should have written that TRIPLICATES are two more than are acceptable, since you already asked this a month ago:

http://www.gamesas.com/topic/1351441-poor-framerate-on-a-new-game-please-help/page__fromsearch__1 )

So how to I update the graphics card and other things that I need to meet the requirements to run Skyrim properly? And how much will I be paying?

Only if it's a desktop, you can buy a minimum card that runs on a stock branded power supply. Laptops are disposable devices that cannot have the graphics upgraded internally, and external solutions are either too slow, or way too expensive.

http://www.newegg.com/Product/Product.aspx?Item=N82E16814141118

That's an HD 5570 for $80, which seems about $15 too high, based on other recent scans through the Newegg offerings, but I have the feeling you just have a laptop, so that more effort would be wasted.

Nope; it is a desktop computer, my friend.

Errrm, am I being thick here but what's the 8800 reference for? What version of Skyrim is she running, and what exactly is this dll supposed to do? What other mods are you running - including the official HD texture packs?

My advice is to disable all mods (easy to do if you didn't install manually), delete your .ini files, get rid of this dll, download and run GPU-Z and monitor the game while it's running by ticking the box. Exit out of the game and look at each of the results fields in GPU-Z, use the drop-downs to find the "max". Turn off AA and reduce your shadows to Low. Let us know.

Here is a $55 card (after rebate) that will work. It's an HD 6570.

http://www.newegg.com/Product/Product.aspx?Item=N82E16814150575