The voltage of AA Ni-MH cells drops under load. That voltage drop can be up to 25%, which can be enough to prevent the camera starting up. This is especially true if charging has been sub-optimal, as it often is with modern high current chargers ('fast charging'). Trickle chargers with a current below 50mA will charge Ni-MH cells to a higher voltage (close to 1.5V) and extend the run time of Ni-MH cells, although charging at this rate can take a couple of days.
Li-ion cells are less prone to voltage drop under load, and so they are a more reliable power source for devices that draw a high current at start-up (devices such as digital cameras).