If the desktop PC has a real video card with its own discrete video memory, then it will probably work a LOT better.
The latest drivers won't suddenly make onboard graphics have 256MB of discrete memory. If the laptop doesn't have graphics with discrete memory, there's not a lot you can do.
You can find out whether your graphics has discrete video memory or not by running dxdiag. Here's a site that has pictures telling you how to run dxdiaghttp://forum.wildgames.com/topic/18740-how-do-i-create-a-dxdiag-and-send-it-to-customer-support/
Follow the instructions up to Step #7. Then instead of going to the wildgames.com website, open the dxdiag.txt file in Notepad (double-click it and it should open in Notepad). Copy the contents and "paste" into a forum post in this thread. Or just email the dxdiag.txt file to one of us and we'll post it for you. Then we can tell you if your laptop graphics meets the game's requirements.