Can you measure the current into the device with your meter ? Depending on the power plug, you might have to solder on a wire. If you meter didn't have current, you could use a really small resistor in series, like a a 1 ohm. It might get really hot, really quickly tho, depending on the current.
Are there any chips near the power in ? Most things these days would have some step down voltage converter(s), with inductors. Have a look around at all the chips, see if they are labelled, look up their Vcc, and you could try to figure out the voltage rails from that.