Hi
Yes you can disconnect the IDE cable from the CD-drive (when the computer is off) and add the 4GB HDD to it, set it to Slave on the jumpers or Cable Select position and bootup. The drive will be picked up by Windows and you shall be able to copy anything over you wish
There's no need to go pocket digging here.
PS: Bear in mind "most" programs won't work if copied over from another HDD, unless they be in ZIP format you copy over or they are not dependent on registry hives on your old HDD. Files/folders will be though.