Many mobos will support both SATA and ATA (aka IDE or PATA). This is especially the case as many DVD / CD drives are still ATA. In any event your mobo may have a spare ATA connector / controller.
So, if your DVD is ATA, you may well be able to connect the ATA HDD on the same cable (the standard cable supprts two devices). You will need to set the jumpers correctly (HDD as master and DVD as slave, or try the canle select [CS] option).
If you have a spare ATA connector on the mobo, you should be able to get another ATA cable and use that instead.
In any event. do you know what mobo it is?