Good laptop for work/play?

I'd like to get a good laptop for both work and play. Think like a "high performance laptop".

I'd like one around say $600-$800.
It should be able to run Skyrim.
Preferably companies like HP or Lenovo. No Dells please.
And with a 1 TB hard drive.

Compare the specs of what is availble to you with these, better if you can find one that exceeds these specs.
-Windows 7/Vista/XP PC (32 or 64 bit)
-Quad-core Intel or AMD CPU processor
-4GB System RAM
-6GB free HDD (Hard disk drive) space
-DirectX 9.0c compatible NVIDIA or AMD ATI video card with 1GB of RAM: Nvidia GeForce GTX 260 or higher; ATI Radeon HD 4890 or higher
-DirectX compatible sound card
-Internet access for Steam activation

For that money you won't be getting an Alienware with a real graphics card crammed inside of it.
So, you'll be using some form of integrated graphics.
The absolute best integrated graphics on earth come from AMD A10 APUs' The A10-7850k being the king. It will run Battlefield 4 at 1080p with no problem. The 700$ intel i7 chip combined with an Nvidia 630M can't touch the 170$ AMD chip solo.
fact, the AMD chip is a quad core with 8 graphics cores as well on the same chip. Over 7 billion transistors. AMD stand for ADVANCED Micro designs for a reason.

Don't drink the intel kool-aid.