I've been playing at noble difficulty but ive come up against a problem.

Early game I'm fine. I can normally take out one of my neighbours with swordsmen or something, and between that and expanding quickly I can be one of the top scoring civs.

After about 1000AD or so, I find I have fallen behind in technology. I've plenty of money, cities and units but I'm so far behind tech wise that I can't defend myself from a sneak attack (which always comes).

How can I stay advanced enough?

Build lots of cottages in the early game. By 1000 AD they should all be developed into towns. Pump out some Great Scientists and use them for Acadamies in your top beaker producing cities. On Noble, if you're the first to discover Literature, you can get the Great Library shouldn't be a problem, even for a non-Industrial civ lacking marble. Obviously, build libraries, universities, and observatories.

You say that you've got lots of cash, which is peculiar. Make sure that you're running the maximum science you can support. I bet the game automatically lowered it when you after that early war, and you haven't raised it back up.