Unless you have a firm grasp on the circuit and electronics in general, you are on a hiding to nothing. Testing components in circuit is complex, because its a circuit and any measurement you make is affected by connected neighboring ones. If you set a multimeter to continuity and put it across capacitor it will show continuity until the capacitor charges up and then it stops. A capacitor is essentially two metal plates with a gap between them - there is no continuity, but it does store charge which is what you are seeing. This is why they are used, they can smooth out blips, or make up parts of filter circuits.
As a very crude rule, if something has failed its quite likely to be in the power regulation stage like a large electrolytic, a blown fuse, a burnt out resistor. Or an IC you can do nothing about because its full of custom code...
With knowledge and a diagram (or measurements from a running powered up board) you can narrow down what part of a circuit doesn't work by checking things starting with the basics like "is it getting power" but without that information you are stuck with spotting the really obvious common stuff like fuses or that part is black and clearly burnt/gone pop.
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