basically everything from that transformer south is the main power supply. It is of the "switch mode" variety. I'll explain briefly how it works so you can test it properly.
You have 4 main parts to a switch mode power supply (SMPS)... a conversion stage, a control chip, a switching MOSFET, and the transformer.
first, the AC from the wall outlet flows into the chassis through the cord and flows through the conversion stage. this is usually a bridge or set of diodes that convert the Alternating current (AC) to a direct current (DC) we now have somewhere around 100 volts of DC.
the next thing that happens is the DC flows to the MOSFET (in the photo - attached to the heatsink below the transformer you pointed out). a MOSFET is like a switch that can turn on and off VERY fast. many 1000's of times a second. we will get back here in a minute.
what also happens is a small 8 legged control chip starts to operate. what it does is monitor the voltage of the system and opens and closes the MOSFET switch very fast. if it senses the voltage going down, it holds the switch open slightly longer, if it goes up, it leaves it closed a little longer. this is called DUTY CYCLE. our constant stream of DC voltage is now being very quickly pulsed.
the output from the MOSFET is now pushed out to the transformer you pointed out in the photo. the high frequency pulses are converted to different voltages by this transformer. (5 volts, 12 volts 70 volts, 140 volts.) for use by the monitor. this section i described is the power supply.
the MOSFET and the control chip have protection built into them to keep from being damaged due to a fault. the chassis will sometimes emit a squeek, squeel or chirp if there is a fault. this is due to the system trying to start up and shut down because of the fault. it senses an issue, shuts down, then tries again...many times a second. usually this is audiable but not always.
you are going to want to check and make sure the MOSFET is switching.
DISCLAIMERthere are some nasty voltages that could kill you if you touch them. use caution when working an open chassis. avoid the large wire suction cupped to the tube and the AC voltages coming into the chassis. generally avoid touching ANYTHING unless it's with a meter probe.
the conversion stage is likely okay since a fault here will often blow the fuse. so we will test the switcher an see what we have. this isn't going to be easy. it might be best to use some alligator clip wires (something like this:
http://www.asia.ru/en/ProductInfo/998804.html to attach the meter probes since it isn't particularly safe to reach in there while it's powered (working or not)
the MOSFET has 3 legs, an input leg, an output leg and a switch leg. called the GATE the SOURCE and the DRAIN. most mosfets have the legs oriented in the order from left to right (when looking at the writing on it) Gate, Source, Drain (GDS). what you need to do is clip the red meter lead onto the middle drain leg and the black lead onto the ground of the chassis. (basically any metal part.) you want to make sure the clip touches nothing but the leg and NONE of the other legs. TRIPLE check. set the volt meter to read voltage over "200 volts DC" sometimes it's best to set the meter to it's maximum rating to be safe if the voltage is unknown.
power up the monitor and see what you have. it should read pretty steady. if nothing, the MOSFET or the switcher chip are bad. if it's all over the place with seemingly random readings it could still be bad or there is something else down the line wrong.