Well, my original post DID have a link to external hard drive enclosures that allowed you to take your SATA drive and plug them into a USB drive. But, if there is a SATA connector on the back of your new computer, I didn't see it anywhere in the pics.
Basically, plug in the old hard drive, go into bios, and set your internal hard drive as the primary drive. Set your old as the slave. You should be able to start up the computer then.