The Foleo's battery is identified as Palm part# 157-10039-00, a li-ion battery with rating of 7.2 V and 3500 mAh. It's a 2P2S configuration - the type is LP103450SP-2P2S. All of my battery packs have self-discharged into a unrecoverable state, and no off-the-shelf alternatives are available. Physically, it looks like the Palm engineering team took the cells from four Treo battery packs (3.6 V, 1750 mAH) and wired them up in a 2P2S config.
The connector to the main board is a set of five contacts arranged as
1 - Vin
2 - plastic pin
3 - ???
4 - ???
5 - ???
6 - GND
From testing with a bench power supply, I'm able to power a unit with 7.2V applied to Vin and ground connected to GND. The unit would act as if it was low battery from 6V to 7V, with no LED blinking at 5V. I don't know much about the charging circuit; there's an adapter input on the side of the Foleo which provides 12V 1.5A with a center-positive barrel jack. With no battery installed, this power circuit is sufficient to bring up a Palm logo on the screen, but some early system check fails and the device resets.