If they both use the standard 110 volt AC cord, I don't see why that would be a problem, but if they don't, you'd just be asking for trouble if you don't use what comes with the computer. And by all means check that user guide!
`
Good luck.
I just got a new all in one PC...2 inch larger screen then the all in one I have now. Can I just unplug the power cord and ethernet cable from the old and plug into new and then follow the set up prompts???? Is it that easy (I hope)

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic