Uh, if Asteroids Deluxe is anything like Asteroids, the hum is gonna be there for all of time.
Seen here(mind you, this advice is all from my Asteroids knowledge)
I've read that if you connect a wire from the frame of the speaker to the ground on the ARII, then you can kill the buzz.
Meanwhile, if you don't coin up, and don't have the panel connected, you can't tell diddly shtuff except that the board is getting power (red led). There are no attract mode noises, so you can't expect something to happen. Also, did you try adjusting the brightness and contrast on the vector?
Turning the brightness all the way up overrides the spot killer (DONT DO THIS FOR MORE THAN A FEW SECONDS!!!!!!!) You can see if you are getting only veritical or only horizontal deflection.
Did you check the board for chips that seemed extremely hot? That means they are bad?
Have you check to make sure that you are getting the correct voltages on the board? If you have a substantailly lower at the board, then you have a harness problem, and you will most likely start to burn your harness contacts.
Also, hook the multimeter to the X and Y test points, make sure they are fluxing!!!
Have you read the Asteroids Repair Encyclopedia? Have you read it multiple times? Have you read it over there? Have you read it eating limes?
Seriously.