Troubleshooting 201:
Check the power supply output at the chips on the board. If not correct, adjust the power levels or replace the power supply.
OK, so you have power.
Do you have something showing on the screen? Do you have sound? Does it play blind? Also, do you have an EPROM programmer? Does the game have a DIP switch for self test?
All these questions determine where you start testing first.
If you have an EPROM programmer then pull each ROM and test it. Use ROMIDENT to tell you if the ROM is a known MAME ROM. If it's not, then use the checksum that ROMIDENT calculates and search Yahoo! or Google for it. Replace any bad ROMs and see if the game works.
Flip any DIP switches for self test. See if the game boots up enough to tell you if a ROM or RAM is bad.
If it plays blind then check the video clock signals and the video output latches, etc.
If it doesn't play blind and the ROMs/EPROMs are good then it gets harder. First stop is to visually inspect the board for backwards chips, broken components, missing components, and damaged traces.
Next, check continuity on socketed components to make sure you don't have bad sockets - these are more common on old games than you'd think.
From here you check the reset line. Z80 CPUs are strange in that the require a longer reset time than a 68K CPU. This can result in the main CPU working and the sound CPU being totally dead. Check the reset line with the logic probe for a good solid low logic state before it goes high. If it's too short the Z80 will never come up.
If it's a 68K CPU check the HALT line. If it's low then there's a bus error and the CPU has stopped. Check the program ROMs, work RAMs, and address decoding logic.
Next check the data signals on the program ROMs and work RAMs. If the R/W (read/write) signals are stuck logic high then the chip is not being written to. If the OE and CE (Output Enable and Chip Enable) lines are stuck high then the chip is not being read. If this is the case then the CPU is bad or the address decoding logic is not working correctly.
Next check the data and address bus lines on the program ROMs and Work RAMs for activity. If any of the lines are dead, check the traces and socket first then replace the chip. You are also looking for lines that simply pulse at a regular interval instead of pulsing crazy with data. If you find those then check the traces and socket first, chip second.
If it's not a trace, socket, or RAM/ROM chip problem and you still have dead lines on the Address or Data bus then check the buffer chips (generally 74244 on address and 74245 on data bus unless you are working on REALLY old stuff with chips like 8T27/8T28) and their respective sockets for problems.
If that's not it then it's a big slimy booger to go investigate all the chips that tie to that address/data bus to see if one has a shorted gate. Also, it can be a major pain to troubleshoot address decoding logic as that tends to involve either a lot of generic 7400 series logic to test or custom PALs/PROMs to do the decoding.
WHEW... With that said, once you get the CPU up and running then any other problems can be tackled separately.
RJ
PS: If you don't know how to read logic gates (7400 series) then I'd suggest you find an online logic primer.