First of all make sure that the new drive is jumpered to be the master one and the old one the slave. Then go into the BIOS on start up and make sure the master is set as the boot drive and that it can see the details of the slave. If that fails try unplugging the cable from the DVD drive and plugging it into the disk drive this will put the drive on a different channel and eliminate possible conflicts due to cable/jumper select errors. It should re-install the DVD drive automatically when you replug it when you've transferred the data across.
The other way is just to network the old M/C with the new one, Share the folders and transfer them that way, or just put all the files onto a DVD/memory stick on the old M/C and transfer them that way.