Memory doesn't seem to be an issue, nor does powering the systems.
Franchise: Star Trek Series: The Next Generation Season: 06 Episode: 12 Title: Ship in a Bottle wrote: RIKER: How did you do it, sir?
PICARD: We managed to programme the holodeck inside the holodeck, and use the same ruse that Moriarty used on us.
DATA: When he was attempting to contact the real Bridge, he was in fact speaking to a simulation.
TROI: You mean he never knew he hadn't left the holodeck?
PICARD: In fact, the programme is continuing even now inside that cube.
CRUSHER: A miniature holodeck?
DATA: In a way, Doctor. However, there is no physicality. The programme is continuous but only within the computer's circuitry.
BARCLAY: As far as Moriarty and the Countess know, they're half way to Meles Two by now. This enhancement module contains enough active memory to provide them experiences for a lifetime.
PICARD: They will live their lives and never know any difference.
TROI: In a sense, you did give Moriarty what he wanted.
PICARD: In a sense. But who knows? Our reality may be very much like theirs. All this might be just be an elaborate simulation running inside a little device sitting on someone's table. Well, we have a newborn star to study. Mister Barclay, you will keep that safe?
BARCLAY: Aye, sir.
(everyone else leaves)
BARCLAY: Computer, end programme.
It always seemed that they never had a hard time building Data new bodies. The problem was making a brain like Data's, but they clearly have comparable technologies.