There are several things you can do to determine faults without a schematic.
First use your nose and eyes to determine smell, cracks or discoloured components.
Check the fuses.
Measure the supply voltages.
Check the supply voltages for excessive ripple.
If you suspect a powersupply failure, check the supply part for shorted diodes, shorted semiconductors and electrolytic capacitors without capacity.
Measure the Voltage on the supply pins of each integrated circuit.
Measure the logic levels on the data pins of integrated circuits.
Check oscillators for correct frequency and output level.
Compare the signals on integrated circuits with the datasheet of that circuit.
Draw a block diagram and try to find out which components are used in each block of the block diagram. Components connected to input or output connections can be found using an ohmmeter.
Integrated circuits with a special function often only fit in one block of the block diagram.
Using this rough schematic and the datasheets and application notes of the components used, you almost have the complete schematic.
High power components and components directly connected to input or output connections fail more often than low power components in the middle of a circuit.
In analogue circuits resistors of 100 kilo Ohm and higher often fail, having much higher value.
In high impedance circuits shorted decoupling capacitors could cause problems.
Open decoupling capacitors might cause oscillations.
If a ”power on reset” circuit fails, a processor might not start properly, resulting in unpredictable actions from that processor.
If nothing helps, try to test every component separately.