I left my GT with the shutter cocked for a few days and this drained the battery - the manual does warn you that this will happen. To check the batteries condition you really need to measure the voltage under a typical load. I've read that the camera presents a load of 100 ohms, so try measuring the voltage with a 100ohm resistor across the terminals. If it's much under the 4.5V, the LEDs won't light