Firstly, if you are a graphics designer, why do you refuse to buy a Mac? They are brilliant for the task and are well worth the investment if you are a professional. Compared to any other platform or operating system, the combination simply cannot be beaten.
This is why you should get one. A major plus is that you would be able to run both Windows and Mac OS X, giving you the best of both worlds.
I don't think the machine you are considering purchasing will be significantly faster. Windows is a resource-hog in its own right, you will never see the true performance of a machine while running Windows on it. With another operating system, like Ubuntu or Mac OS X, you can.
There are free alternatives to the large and bloated commercial software applications. Firstly, there is
The GIMP. It is a raster graphics editor similar to Adobe Photoshop. Next, there is
Inkscape, a vector graphics editor similar to Adobe Illustrator. And finally, there is
Scribus, a desktop publishing package similar to Adobe PageMaker or InDesign. There's no doubt that Adobe have years of experience in the visual arts software market. However, their software is expensive and can be difficult to use.
If it was me, I would probably keep the existing machine, install Ubuntu and the three applications I mentioned above: The GIMP, Inkscape and Scribus. I'd learn their ins-and-outs and then apply my (absent) graphics design knowledge to create unique projects. :)