First verify that your power supply really corresponds to the one I have. If not, you should mark up changes especially in part designators and post your drawing for future discussions. You refer to 2.7V output; that I do not have on my drawing.
Highly abbreviated theory of ops: C1 is charged by bridge to provide main DC power to be used by switcher. 150K resistor provides initial current to start up AZ3842 switch controller chip. Pin 6 drives Q1 power FET switch full on and full off, but with inversely varying duty cycle according to an opto-isolated sample of the 3.3V output, which is the only one output that is voltage regulated. The rest go as turns ratios of the output windings. Q1 drives the primary winding of the transformer, which has a dedicated winding and D7/C2 power section to more robustly drive the AZ3842 continuously without overheating the 150K startup resistor. All other windings are rectified to provide four different STB DC outputs
Taking care to avoid electric shock, what DC voltage do you have across C2? Should be at least +12V and less than +25V across C2, and make an AC measurement also to verify very low mV of ripple. If there are problems here, check the 150K resistor value, check D7, replace C2. If C2 shorts, it can then short D7 which can then ruin any replacement C2 you install. If you measure different values of AC ripple when you reverse probe polarity, report this also; some multimeters inaccurately report AC when measuring in the presence of DC voltage.
You can also turn the thing off, verify C1 has discharged, then measure the transformer sections to verify 1.88 ohms primary, .73 ohms bootstrap power winding, and then with respect to the secondary ground terminal, the .22 ohms, .05 ohms, .04 ohms, and 1.25 ohms output windings. Subtract the measured resistance value of your probes when shorted together to get a more accurate reading. You may have to clean your probe tips with steel wool and scrape any insulating film off of the solder pads under the transformer to get consistent readings. There better be continuity in all windings and no leakage between windings not sharing common terminals.
More info can be had by downloading the AZ3842 pdf datasheet from www.alldatasheet.com
or similar site.