I exclusively play Society, so this issue would most likely never come up, but I'm still curious. Could you still use a powered weapon even after losing all of its charge? I mean, some weapons like the flame doshko and cryopike exclusively deal their respective elements' damage so I could see why those might not work, but then there's things like the Dragonglaive from Alien Archive that deal a physical damage type on top of their element and are clearly designed to be an enhanced version of an already existing weapon and would seem perfectly capable of damaging things on its own, powered or not.
RAW, how would this situation pan out?
Per the Powered weapon property, using such a weapon when it has no charges means it is treated as an improvised weapon.
If you're using an object that wasn't meant to be used as a weapon, treat it as a club. You don't add your Weapon Specialization bonus damage (if any) when attacking with an improvised weapon. At the GM's discretion, the object might deal a different type of damage or not be treated as archaic (see page 180), and in rare cases a GM might decide a nonweapon functions as a specific weapon (such as an industrial grinder functioning as a fangblade). In such cases, attacks with the weapon take a -4 penalty to the attack roll because of the awkward nature of attacking with something designed for another purpose.
One of two things will happen. By default, an uncharged powered weapon will function as a club with no specialization bonus damage - 1d6+Strength. Alternatively, at the GM's discretion, it may deal a different amount or type of damage as if it were a different weapon altogether, though with a -4 penalty to attack. Weapons such as the dragonglaive are examples of where such GM discretion might come up, but it is not guaranteed.
Note that Powered melee weapons drain charges per minute rather than per attack, so you will hopefully not be faced with this problem too frequently.