re: Swapping hard drive from one laptop to another...

You can generally get around hardware driver conflicts by uninstalling old drivers and replacing with the correct ones without too many issues, especially in Windows 7 and above (though it's still best practice to do a clean install). But, the biggest issue you're going to face, with no way around it, is the OEM license. Your Gateway came with an OEM version of Windows tied to that vendor and most likely the bios on the Gateway's motherboard, and it's not gonna activate on the Asus.