These two posts capture the essence of the process for me too. You don't need to know everything there is to know about something.
First you collect information on what is happening when power is applied with your DMM and compare it to what is supposed to happen as laid out in the datasheets for its individual parts. You can also make some additional tools . Since your board is a switching power supply, be careful.
As it has at least one microprocessor on it, you will want to see if the microprocessor(s) has any "heart beat". This may not be as easy without an oscilloscope as it would be with one. Especially, watch out for high voltages. If you plan on doing electronics a lot, try to find a deal on an older scope.
That will give you a good start on it. Keep in mind the sage advice to doctors. "First do no harm". Don't break anything additional. Use common sense and think when probing the board. Measuring voltages properly is unlikely to cause any damage. Check if voltages that are supposed to power various parts are even there. If they are not, its likely there is your problem.
Even parts that are soldered to a PCB are replaceable. Just watch how Louis Rossman does i in his Youtube videos. (To do that you will need to invest in tools to do it but they are not so super expensive that its difficult. Several tools that work well, either alone or combined with your regular soldering iron are a digital hot plate for preheating, a controlled temperature hot air gun, and ChipQuik: low melting point solder for removing SMD parts, all individually can be quite cheap)
If you fix it - every time you use it you'll get a jolt of satisfaction from having done it.
I understand that it is easy to look at a mass of parts and think it is just black magic. Diagnosis is an art. You make a list of what you know and what you don't know about the problem. A power supply is just made up of a bunch of simple blocks. It is a logic chain you work through. A bad photo tells you enough, look in this section. Don't think the OP has detailed the problem beyond "It's broken." The OP needs to step up and approach this logically.
The beauty of learning to troubleshoot is that it's a universal skill. If you can troubleshoot one thing, you can troubleshoot another. Though it helps to have specific knowledge on the subject, it's not actually needed to get anywhere.