There are a number of tools that claim to be able to do this: Take a running installation on one system and get it running on dissimilar hardware.
EASEUS To-Do Backup has a "Restore to dissimilar hardware" option. Windows provides a sysprep.exe tool that basically sets the drivers and certain other information back to the just-installed state; you actually go through most of the installation menus, including entering the product key. I would have more faith in this than in other approaches. http://www.sevenforums.com/tutorials/135077-windows-7-installation-transfer-new-computer.html
That said, if I were in your place the very next thing that I would do is to buy a faster drive and clone your now-adapted-to-new-hardware system drive onto it. If the new machine is a desktop, you've got room for a faster and bigger drive.
Let us know how it goes.