Some additional details would be helpful.
Version of Windows
Make and model of the DVD drive
Version of WinDVD
First, the primary drivers for any IDE drive be it CD or DVD are handled by the IDE driver for the chip-set on your motherboard. No further drivers should be needed.
Second, if your new PC has Windows XP, make sure that you have the updates and / or service pack 1 installed.
Also, make sure that the version of WinDVD that you have supports Windows XP.
You may simply need anewer version of WinDVD.
Third, on the old PC, did you use a hardware decoder card?
Many early DVD drives were sold with hardware decoder cards. Your drive and or software may be looking for the decoder card.
Chas