You might just try connecting an LED (with a current-limiting resistor, of course) and run it for a few hours to see if something happens.
If you've got a mulimeter, I'd also recommend checking the voltage with and without a load to see if it's regulated. And, assuming you don't have an oscilloscope, put a load on it and measure the AC voltage to check the filtering. (Pure DC will measure zero on an AC scale.)
...Chargers don't have to be well regulated or well-filtered, but they should be current-regulated (and short-circuit protected).
If you don't have a multimeter, leave the LED connected and check to see if the LED dims when you add a load.
You know Ohm's Law, right? If you want a "known load", 8.4V with a 16.8 Ohm load would be 500mA. And, you'd need a 5 or 10 Watt resistor (8.4V x 1/2A = 4.2W).