How to check microprocessor whether its working or not

Hello

i am working as repairer i repair control cards of weaving loom machine but i don't know to test microprocessor of control card is working or not any suggestion. i am able to check test power electronic components etc.
please help me
for example this card

First off all, in the lack of proper documentations of the board, you have to search on the web for the microprocessor's pinout, and probbing someones by scope. I'm assuming that you have enough knowledge to know that special care must be taken when handling the board energised, particularly in regard to components like memories which you should skip if possible.

Yes your right proper documentation is important before handle the board.
The things is in all control cards microprocessor held in reset state by external WDT untill self test and safety conditions will not completed in that case control card give error message and turn on red led. But in some cases control card remain in reset state even safety conditions are turn and core microprocessor doesn't communicate with main CPU card also not give error red led. So that would be further step. Any suggestion

I am not aware of the application for what this board operates, but if you have bad luck, the basic operation of the board (read, active signals) may depend on the electric external conditions, what means that you should have to build a Giga, or even make tests directly connected on equipment. In the worst case, could also depend on communication with other intelligent modules, being complete OEM or embedded systems. In shorts, if the basic probing previously suggested not suffice, you'll have to deal with a lot of effort

The minimum information needed is (i) what it is supposed to do. It needs some set of input and it produces some set of outputs. If you have the all possible outputs for all possible inputs, you know the transfer function and that can be used to test whether the card (as a block unit) is working or not. The documentation will not have the circuit details but will tell what pin will have what voltage under what conditions.

First test is a visual inspection: if any component has gone bad (visibly). If the microprocessor is running, you will be able to figure out from the pulses from some pins (the documentation for the microprocessor should be easy to get from the internet), then some other component is gone. Your board looks clean but a thorough cleaning and connecting only the power pins can be a starting point.