Create a new folder on you new drive. Or, if you prefer, create a new partition.
For now, let's go with the new folder. You may need to unplug other devices to make the system more stable. The happens. Un plug completely the CD-ROM. In fact, put the drive on that cable, if it is that type of drive.
Now you should be able to open the drive with Windows Explorer and just copy files to the new drive. Avoid using move, The are issues with moving lots of files between two drives and we don;t want that hassle now.
If you run into problems, try moving smaller hunks. Patio said there is a 2GB limit on the copy in Windows Explorer.Or something to that effect. Most of the stuff you want is the the My Documents section of the user you named on the old machine. Look in Documents and settings. Maybe called James' Documents.
IME old hard drives put a burden of the power supply and the IDE interface. I am not sure why, but I just unplug drives that are not needed during the copy process.
When you are done with the copy, power down, you knew that, and put things back the way they were. Power up and you can start making copies of you old stuff to a DVD-R. Never use DVD-RW. Unless it is photos of you mother-in-law. (Just joking. Ha Ha)