i gotta agree with the lebowski, if you don't know how to get the case open and cannot tell which terminal is which on the input caps then you have to go through just one side of the rectifier diode bridge by connecting through the AC terminals.
but for those interested, if the AC adapter, or charger brick as they are generally known, will not work at the lower voltage on the input, and it will not start oscillating even if you do put the voltage right on the input caps, then there are mods you can still do in order to try to make it oscillate.
the pwm IC current controller has a pin that is used to kick off the oscillations as soon as the power is turned on. there is one leg that comes off the transformer and goes through a 5meg-10meg resistor directly to one of the pins on the pwm IC current controller. you may be able to make it start oscillating if you can reduce the value of that resistor by putting another in parallel, by soldering another surface mount directly on top of the other surface mount resistor, or soldering a leaded resistor across it. the idea is to get more current to the pwm IC in order to get it to start oscillating.
you can also reduce the value of the gate resistor if there is a separate mosfet for switching the DC current in the front end through the transformer. but most of these tiny charger bricks have the mosfet integrated into the pwm IC and you cannot change the gate resistor. but if you can get to the gate resistor, and changing the kick start resistor did not work, then you can add another resistor in parallel with the gate resistor to see if the mosfet will then turn on and off fast enuff. maybe even change the oscillator frequency on top of that, all to make it work at low input voltages.
but if you are down below 60V, then the 2596hv regulator will work and you should be able to find cheap 60V max DC-DC converters without using a charger brick and you would then be able to adjust the final output voltage too.