Board level repairs are near impossible without a schematic and an engineer level of knowledge to calculate nominal values at different measurement points. You can measure resistance of certain components and compare to their color coded value but as often as not will end up destroying a sensitive IC chip through back probing- the meter sends a voltage to measure resistance and it gets to a pin on the chip not designed for it. And with SMT components replacement is impossible without specialized micro tools anyway.
When a power supply board goes bad about all you can do is inspect for bad caps, which will appear swollen/leaking, and do a visual with light and magnifier on any through hole solder joints. Usually input jacks or large wires to other boards.
I have repaired a number of PC LCD monitors with bad power supplies on the illumination section that had visually obvious bad caps. Mfr (usually viewsonic) used low bidder substandard caps. $9 in parts an hour labor and good for life. Never hurts to take em apart and have a look.
If you want to get crazy and the boards happen to be that lead free euro safe solder which is prone to separation, cracking and tin whiskers, you can try throwing it in an oven at about 425 degrees or careful direction of a heat gun. Basically resoldering the whole board in a similar way as the SMT components originally were. Many XBOX360 owners reported success with that in repairing RROD issues. However that is obviously an unorthodox unprofessional method with as much chance of utterly destroying your equipment as fixing it. Last resort before the round file.