Unless the power brick has an output of 7.2 or 3.6V I suspect hooking it directly to a Li-Ion battery would be a bad thing, with lots of fire and exploding. If you take a look at digikeys website they have assorted Li-Ion charger dev. kits (Microchip or TI), one of these could be used to recharge the battery safely. Be prepared to do some technical reading though.
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