Here's the resolution to the non-charging Duo battery problem repeatedly discussed on comp.sys.mac.portables. This problem is real, verified in several discussions with 800/SOS-APPL and one $30 visit to an "Authorized Repair Shop" with my brand new Duo 250. Unfortunately, I couldn't find my proof of purchase in the clinch.
The symptom is that the Duo refuse to charge its battery, though it runs fine on external power. The cause is a still-mysterious conflict (mysterious to Apple as well; they're still tracking this one down) between the recently released PowerBook Duo Enabler 1.0 and the Express Modem software, both of which came pre-installed from the factory in my case.
The result of this combination is that sooner or later (the trigger is unknown), something low-level that controls charging becomes corrupted such that none of the standard "reset the world" tricks can repair it (zapping the PRAM, resetting the Power Manager by holding in the reset button for 20 seconds with the battery out, resetting the Power Manager by leaving all power sources disconnected for an hour, etc.).
The fix is to completely remove all power in order to clear the corrupted bits. There's a slow way and a quick way to do this. The slow way is to remove the external battery and leave the Duo unplugged long enough for the internal lithium battery to run down. You can also send the whole thing back to Apple for a warranty repair in that time since we're talking about two days or more.
The quicker way is to remove the external battery and unplug the internal lithium battery for about 15 seconds. To get to the internal battery, you must remove the keyboard by removing the three screws that hold it in with a Torx T8 driver - auto supply stores generally have it. The three screws you want are towards the back of the Duo (there's a fourth towards the front under the trackball that needn't be disconnected.)
The tricky bit is disconnecting the internal lithium battery. Its connector sits under the right end of the space bar; it's the connector with three multicolored wires leading in. The connector is so tiny I couldn't figure how to disconnect it, which is why I gave up and took it to the shop. It turns out that the connector unhooks by motion parallel to the circuit board best achieved by using two small screwdrivers to push against the two wings provided for this purpose.
All this (except the do it yourself part and the connector disconnect drill, which I learned by spending $30 to watch the repairman do this) has been verified with 800/SOS-APPL. They're working on curing the problem at the root, and will release a new PowerBook Duo Enabler and/or Express Modem Software kit when they do.
Be very careful if you try this fix yourself since you are guaranteed to void your warranty if you blow it. Things are delicate in there.