Your new machine has a SATA (Serial ATA drive) connected with a small cable to your hard drive.
You will probably find that you have a DVD/CD Burner connected to an EIDE cable. EIDE uses the old flat 80 pin cable.
You should be able to connect your old hard drive on the same EIDE cable after making sure that the optical drive and the hard drive are correctly configured as master and slave. PM me if you need further help.