When the son of Phoebe Halliwell and Cole Turner was stolen by the previous Seer, it was believed that the unborn child had been killed by an overload of his powers. This was not exactly true. What happened is not completely well known, but what is known is that the child found his way into the womb of a witch also nearly four months along.
This witch was Monica Gray, her husband had been killed in a car accident shortly after she found out she was pregnant. Monica was surprised to discover she was carrying twins, but presumed it had simply been an oversight by the doctors before.
When Dorian was born his powers seemed to be much weaker than they had been during his time with Phoebe and the Seer though this was due to the incredible strain it had put on his developing body. As he aged he grew into his powers slowly, first Pyrokinesis.
His mother Monica was worried when her son developed this ability as it was almost always a sign of evil, or at least a trying and troubled life. But she loved him never the less and worked with him to keep it in check, to now how and when to use it.
When Dorian was 5 a demon attacked Monica. Out of instinct or reflex Dorian pelted the demon with a fireball seriously wounding the demon. After it picked itself up off the floor it made to attack Dorian before the little hybrid launched it into the wall with his fire throwing. Because he was still young his powers were not quiet as powerful as it could be and it required Dorian to use both hands to slay the demon.
It was after this that Monica knew something was wrong. Using magic and consulting with other local witches she discovered that her son was part demon, and a powerful one at that. But she realized if his first instinct was to protect someone he couldn't be completely tainted by evil.
She couldn't give him up either, as he was her son even if she was not genetically connected to him. She loved him and raised him with all the patience she could muster, even if he burnt her drapes when he had a tantrum from time to time.
As he got older Dorian developed empathy as a power, while at first a struggle it was his mother and sisters love for him that allowed him to find a strong base to continue to grow and learn to become a proper witch, using his demonic powers to help those he found. However, helping might have been a reflex he still didn't like the idea of being bound to a fate outside of his control.
It was not till many years later that he discovered where his bloodline actually hailed from. And while he is interested in getting to know that side of himself, he feels it is a betrayal of his mother Monica and all she did for him to just embrace them. However, after finding out that his father also possessed the surname Turner he felt it wrong to embrace that name and abandon the goodness that Monica fostered for so long. So with her blessing he took the name Halliwell, though he has yet to really try and connect with that portion of his past.
Due to his lineage he possesses an extraordinary number of powers and abilities. On top of the ability to brew potions, cast spells, and scry as any witch can do he possesses: Flaming, Fireballs, Fire Throwing, Advanced Fire Throwing, Pyrokinesis, Electrokinesis, Telepathy, Empathy, Telekinesis, Possession, Transformation, Sensing, and Super Strength. Though these powers are not all from his demonic bloodline, it appears that Telekinesis and Empathy are native to the Warren Witches, and his biological mother Phoebe possesses Empathy.
While it may be possible for him to develop more of the powers of the source it appears the dilution of evil has cut him off from some of the sources powers permanently while giving him access to his witch abilities and the Charmed destiny.