What do you mean "since it died"? The desktop or the hard drive?
One, if the hard drive died, plugging it into a laptop won't make any difference...
Two, if you plug the hard drive into the laptop SATA connection, won't your main hard drive be disconnected, with no OS to use to transfer the files? Windows is not transferable from one computer to the next. I have never seen a laptop with an external SATA connection.