SFX and Voice data on that board is stored on two 42-pin Mask DIP ROMs located at positions 6N and 6P on the main board (not the ROM board). They'll be labeled VOICE0 and VOICE1 on the PCB.
Carefully pry each ROM out of the socket with a small, flat screw driver. Spray out the socket with compressed air. Inspect the legs on the ROM and see if they look dirty or tarnished - if so, you can carefully scrub them clean with an emery board. Reinstall the ROM, making sure that the orientation and positioning is the same as in the photo, and with none of the ROM legs sticking out. Repeat for the second ROM. Reinstall the ROM daughter board, power up, and test it again.
If you still don't have SFX or voices, you'll want to dump each ROM with a chip programmer and compare the dump against the same file in the MAME romset for the game. The ROM set is named "machbrkr" and the files are "mb1_voi0.6n" and "mb1_vo1.6p" for VOICE0 and VOICE1 respectively. They should dump if the chip type on the programmer is set to a 27C160 EPROM.
If one or both of the dumps don't match the equivalent MAME files then the ROM chip might be corrupt. The mask ROMs were manufactured by Fujitsu and unfotunately Fujitsu has a poor track record with their chips on arcade hardware. A 27C160 EPROM can be programmed with the file data from MAME and installed in place of the mask ROM in the socket. Both ROMs have to be correct for the SFX and voices to work.
If you want replacement 27C160 EPROMs programmed, I can do it for you for just the cost of parts and shipping.
One more thing - make sure the two jumpers to the left of the VOICE1 socket are present and set the same way as in my photo. If either of those jumpers are missing or set incorrectly then the SFX and voices won't work.