There is an old piece of software called "Laplink" which came with a special cable for connecting two PC via the Parallel (printer) connectors. This programme can be run in DOS or windows. (Not sure if it would work with Windows XP however). With this you can set one PC as host and the other as a server and share files between the two. Should also mention, this method of transfering files is very slow as the baud rate is somwhere in the order 9600 transfer rate, if memory serves.
Another possibility is, if you have a spare hard drive you could install this to the old PC to the secondary IDE interface, transfer the data you want to it then transfer the hard drive to your new PC (secondary IDE interface) and collect all the files this way.