Test your frame transistors. Google how to test transistors with a DMM if you are unfamiliar.
If D608 was burned, test Q606 and Q607. Either may be shorted (though this could be from one of the frame transistors being bad also).
The test switch is just a standard on/off switch. You should get the test mode working first, as if the game board isn't working, it may be putting out bad voltages to the monitor, which can cause it to blow.
You should try to get the game playing blind first, by setting the dips to free play (see the manual), and seeing if the P1 + P2 buttons flash. Leave the monitor unplugged until you can get the game playing blind.
If you have an Asteroids cab, you can test the AD board in it. But that's the only other cab you can plug an AD board into to test it.