Your key may still be available in your registry. You might install
SIW (from our
Freeware DB) and run it to see if the key is listed under licenses, I know my Cyberlink PowerDVD 8 still shows up in there.
If the key is available then all you really need is the installer. I found
THIS which says it is for a free demo but if the key is there it may turn into a full-blown version; I don't know but might be worth trying.
And I like apathy's idea of simply explaining the situation to cyberlink and see if they can help. Since the current version is 8 they might not be too concerned about giving away an old version 6.
You might also consider alternatives like IMGBurn - links are available in our Freeware DB.