If a consumer electronic device suddenly refuses to power on, it's a failed electrolytic capacitor most the time (in my experience). Finding them requires effectively no knowledge of circuits. Sometimes one is visibly deformed/exploded, but I usually just replace them all.

If that doesn't work, yea you pretty much start testing things with a multimeter starting from the power source. But if it isn't a capacitor failure, it's probably ESD or power-surge related damage and not worth trying to fix.