Power Regulator Circuit (Game Boy Advance)
The GBA has a single power regulator that generates the 3.3V, 5V, 2.6V (RAM), -15V (LCD), 13V (LCD) voltage rails.
In short, the power comes in from the battery (through the battery springs, fuse, power switch and current limit resistor R33.
Over Current Protection
When there is an over-current detected on one of the outputs, the regulator will shut down preventing any power rails outputting power.
If you get a quick flicker of the power LED then off, use a bench power supply to inject 1V into each output rail (test pads labelled VDD2, VDD3, VDD5, VDD13 and VDD-15) and check for excessive current on those outputs.
If you find no shorts, then check the transformer T1 is not internally shorted (top pins 1 and 3 should be shorted together, but not joined to pins 2 or 4. Bottom 4 pins should all be shorted to each other but not to any of the top pins).
If T1 is good, check L1 has continuity.
From a working console when turned on, here are the expected voltages on the regulator.