Are you using the old hard drive in the new computer, or just transferring the files from the old computer to the new computer (leaving the old hard drive out of the new computer)
If you're going with the first route, be sure to back all your stuff up first before putting the hard drive into the new computer. You have a few options when installing the Windows 7 on the old drive if that's what you're planning to do. There's a step in the install that will ask how you want to install the OS, either on a new partition leaving everything in place (which will save your stuff in a Windows.old folder), or if you want to delete everything on the hard drive currently (known as formatting - which would be recommended) and start from fresh. If you start from fresh, you'll need that backup that you started with to put all your files back onto your computer.
If you're doing the second option and just moving the data, then just do that. Get a $20 cable from a local computer store that foes from SATA to USB and transfer your files over and lose nothing.
Hopefully that helps.