I did a test over at SystemRequirements.com to see if The Witcher would run on my Lenovo laptop, and even though all the specs seem to be up to snuff the test failed my graphics card on minimum requirements and my processor on recommended requirements.

I have an Intel HD Graphics card that meets all the requirements.
1.8GB RAM
Hardware T&L
Pixel Shader vr5.0
Vertex Shader vr5.0

My Processor is an Intel Pentium CPU 2020M 2.4GHz out of the Recommended Core 2 Duo 2.13GHz.

I just wanna know if the game is going to take issue with my Graphics and Processor despite meeting the minimum specs.

Don't trust SystemRequirements.com. They're regularly wrong.
I'd guess it'll run, but you might have to lower the in-game graphic settings. Though Intel HD graphics are a common source of issues with games.
Why don't you try to run the demo? Just search for it, it's available on several sites, e.g. here:
http://download.cnet.com/The-Witcher-demo/3000-7536_4-10784034.html

Demo! Good suggestion. I should have thought of that. Yeah I know SystemRequirements can be sketchy at best and to say that Intel isn't the best choice for pc gaming is a bit of an understatement. Thought it best to ask here.

Best thing I can do is run the demo. Thanks, I hadn't considered that.