I'm wondering with the DMD issue that the problem is in the CPU board and not the sound board. Give the caps a good inspection on it yet?

Edit, take a look at the 6821 PIA at 7B, looks like it does double duty for sound and display.

LW3_2 (resized).png

How do the other boards look? Do any others have signs of previous repairs?

Watch it on boot up, I found this for how it should behave

"At power-on, the CPU board performs several self tests. While watching the LEDs (Light Emitting Diode) on the CPU board, some information can be derived from them. If all the self tests pass, the LEDs illuminate in the following order at power-on.
PIA (Peripheral Interface Adaptor) and +5 volt LED turns on immediately. After about 1/2 second, the PIA LED turns off. Blanking LED turns on next. +5 volt and Blanking LEDs will stay on (until the game is turned off)."

Also worth looking into the sound board chip as suggested and the condition of the sockets on the sound board.

Is it possible you just aren't catching it flash during the boot? Should only be on for a half second. You could also consider picking up a test rom to help troubleshoot this if you confirm its not lighting https://www.marcospecialties.com/pinball-parts/965-0100-00