Some advice to original poster.
- Double check that the original charger was indeed the 10W iPad charger
- If it is the "folding prong" type, fold and unfold the prongs a couple of times to rub off any corrosion that might have formed.
- If it has the detachable prongs, (multi-country type), slide them off the adapter brick, and slide them back on.
- Unplug the cable from the adapter itself, make sure there's no lint or debris blocking one of the pins.
- Inspect the 30 pin connector that plugs into your iPad for lint/dirt.
- Check the cable in between the brick and the iPad, swap it with the cable that came with your 3GS charger brick. (The cables for all of the adapters after the original iPhone are the same, just the adapter bricks themselves changed.)
Since you are getting some kind of signal from the original adapter (as you said you get the lightning icon over the battery), it's possible that there is a bad connection somewhere along the line sucking juice. That's why I focused my suggestions on the various mechanical connections.
Your 3GS adapter is only 5 Watts if I'm not mistaken. It will charge your iPad, but very slowly, and I do not believe it will be able to "top-off" your charge like the 10W adapter will.
If it still doesn't work after all of the above, bring the adapter to an Apple store. (walk up to the Genius Desk) They might replace it for you for free. if not, an extra adapter is fairly cheap.