I'm not sure from your descriptions exactly what your problem is so checking a few basics is in order.
When you turn the game on you should get a high pitched dual squeal. This is normal and tells you sound is working.
In the backbox there are four boards with LEDs on them. Lower right is MPU. Upper right is display controller. Middle left is sound board. Upper left is aux sound board. The LEDs on these boards should all be blinking - not at the same rate or in unison - but blinking. This tells you you have 5v going to your boards.
On the playfield the insert lights should be flashing in attract mode. If they are, you have 12vdc and you know that the two low voltages necessary to drive the display are present and the MPU is working.
Let the game sit and observe the display. It should change in attract mode and say Premier, Gottlieb, Capcom and other things. If it does you know the logic section of the display controller is working an dtalking to the MPU.
If while it is sitting there the display goes out and nothing appears on the screen anymore, look at the LEDs on the boards. Are they all still blinking? Look at the insert lamps on the playfield. Are they still flashing? If the answer is yes, then there are two possible problems.
1 - you have a high voltage problem on your display controller.
2 - you have a bad DMD display.
Of the two, #2 is more likely because if the display first turned on ok but then goes out, your voltages are probably fine since they typically don't start out ok then fade away. Nonetheless you should check the voltages when the display is out following the instructions on Pinwiki: