Old water won't contain enough bacteria to help you cycle.
The quickest way of setting up a new tank, when you have an established one, is to get a source of ammonia into the new tank. Use household ammonia, if you have it; you don't need much, 1ppm would be plenty. If you don't have ammonia, you can put a prawn in (in a mesh bag of some kind, so it doesn't make too much mess!), and leave that for three or four days, until you get an ammonia reading.
Then, once you've got a positive ammonia reading, you add 'some' (I'll define 'some' later on
) of the cycled media from your mature tank. Test for both ammonia and nitrite next morning and, if they're both zero, you know your bacteria are working and you can start (slowly!) stocking.
If they're not zero, then you have to continue as you would with a normal fishless cycle, or you can try more media.
By 'some' media, I mean at least a quarter of your current filter's total, and no more than a third. Don't forget to replace the media you've taken out with some new stuff so the bacteria can spread out again.
The stocking in the new tank will depend on how many fish the media was supporting in the original tank; so, for example, if you have 20 neon tetras in your tank, and you take a quarter of the media, you can put five neon sized fish in the new tank.
Hope that all makes sense; it sounds more complicated than it is, but you're basically moving a small amount of bacteria to the new tank to support a small amount of fish. The ammonia is just to 'prove' the bacteria are working before you risk putting fish in there.