These can be checked in circuit but that will be little bit advance.
Usually it requires shorting base/gate pin of the transistor with emitter/source pin and observe voltage on collector/drain pin, the voltage should rise, then connecting positive supply on base/gate through a 1k resistor the voltage on the collector/drain pin should fall. These have to be done when the board is powered on. This is only one test that I know, there might be others.
Also if you somehow source an another working board like this, then yours can be repaired, it becomes real easy when you give a working board along with a non working board to a repair man, but I suppose chances of that happening is nil.
First you have to get the part number from the transistor, for that you have to remove the heatsink I think. Through this we can see what kind of transistor it is and we will also know the exact pinouts, then you can look for replacement.
You can also try finding the schematic of this board online, it will be helpful for the repair guy.