If my info is correct, impaling a vampire's heart in oWoD paralyzes it until the stake (or whatever) is removed. Could he still use mental disciplines such as Auspex or Dominate?
A vampire immobilized by a wooden stake "is conscious (and may use perception powers, such as those in the Auspex Discipline), but may not move or spend blood points." (p.280, V20)
So, Auspex is definitely okay. Use of Dominate is potentially possible, but would require a power that neither requires you to speak (can't move) or make eye contact (because when you can't move, it's easy to avoid a vampire's gaze). If you've got Auspex up to 5 and Dominate, it's possible to overcome this problem—a manifest Psychic Projection can use Dominate with at least 3 successes on the initial Projection roll.
Elder level abilities open up even wider vistas: The Dominate level 6 power Obedience would allow for this if the character's skin is touched. Light and even brief touches will suffice. When handling a staked Kindred it's hard to avoid skin contact unless explicitly stating it.