I suggest you think very carefully before going down the route you propose. The old disk will certainly be much slower than the new one, (asuming you can get it to work) and with 40GB in place you do not need the extra 4GB. If your old hard drive has an operating system on it, do you really want to transfer it? I suggest you install any programs that you want to transfer from the old hard drive, by using their original installation disks, and then go carefully through the contents of the old drive using Windows Explorer, and transfer any useful document files to floppy disks and install them to the new system from the floppies. I doubt it will take you much longer than transferring the hard drive, and it will avoid transferring all the old useless files that disk drives accumulate. I have much the same new system as you, and I took the route I have described. If you have files that cannot be put on to floppies it may be possible to connect an external parallel port device like a Zip drive, a tape drive or even a parallel port CD writer to the old computer. Remember that Windows backup will compress files, this enabled me to move some large CAD drawing files on single floppies.
Best of luck whichever route you take.

It sounds like you new system has the new ata66/100 cable connected to the hard drives(new faster drives)
There should be 4 connectors for IDE 2 for hard drives and 2 for CD rom drives.
if not you need a new cable. there should be two cables comming from your mother board.
Make sure the Jumpers on the 4g disk are set to slave.
The ribbon cable looks wider but the connector should be the same size. The new faster ata systems is backward compatible for slower hard drives.
Connect the old disk drive to the IDE cable that is connected to your mother board and instlled 40gb Hard drive. The jumpers on this drive should be set to master.
reboot the machine and go to the bios set up. Make sure the ide settings are correct to select master IDE to boot from.
You should then be able to resart the machine.
you will have a new drive letter.
you can then cop the files you need to your new hard drive.
Then delete all the files on the old hard drive and use it as a backup for all you important files. You can use a batch file to copy the files or use the backup software.
Regards Steve Knight