|Backing up to an internal hard drive is better than not backing up at all but not as good as using external media. |
As far as the old hard drive goes, why use only the D partition? If you are not using that drive you can delete all the partitions and use the entire drive.
If the drive still installed in the old computer? If so, did you ever create the restore disks for that D partiton? If not, it wouldn't be a bad idea to do that before nuking the partition.
You can get a USB docking station for your old hard drive. Be sure to get the correct interface (PATA/IDE or SATA). See the link below for a good choice. The link below is for SATA drives.