Right...
I think I realise where you are coming from. By "old" you don't mean Geoffrey of Monmouth, I don't think.
Would I be right in thinking you're getting your stuff either from Iolo Morganwg (Who historians widely think was a forger, but I think may be wrong to dismiss entirely out hand) or the more recent and popular Adrian Gilbert, Alan Wilson and Baram Blacket ("writers" of books like "The Holy Kingdom", "The quest for the real King Arthur" and "The Orion Mystery")?
If it's the later then they are mildly entertaining but full of rubbish, and no serious historian takes them seriously. From memory some of there arguments seems to be based on nothing except speculation.
Is the general premise that the Kings of Morgannwg were male line descendants of Cunedda, they were the true "high Kings" of the Britons and that they are survived in the male line by people with the surname Morgan?
If that's even close then I don't think I'm going to convince you otherwise or that this thread is the place for it.
Enjoy your journey into Welsh history and keep in mind that not everything everyone says is true- even reputable historians are proved wrong by new discoveries.
All it takes is Cunedda's wife(/lovers) to have been unfaithful and maybe none of his DNA got passed on even as far as his children.
Check your assumptions too, they can leave blind spots. Surnames didn't exist in Wales until the 1500's. So for example having Morgan as a surname means that your father's first name was Morcant when that family took on a surname. It's not like the clan system in Scotland is assumed to be where everyone is descended from a chief (and in actual fact it's not like that at all, most clan members are not descended from a chief but merely gave allegiance to one and took their chief's clan name as their surname, but that is the common assumption)
If you have Welsh ancestry then there's every chance you're descended from someone royal, it won't get you a throne but there's every reason to be proud of your heritage.