First -- welcome!
First step is to get yourself a
copy of the manual. The troubleshooting instructions there are pretty good.
Next thing is to get yourself a multimeter so that you can test voltages at various places. You don't need to spend a ton of money on one, but, if you are going to work on arcade games (even if only one game), you need to have one of these.
This will all seem a little daunting at first, but basic troubleshooting isn't that difficult if you take it a step at a time. You will need to have some basic knowledge of
how to use the multimeter and some basic electronics knowledge.
You have come to the right place as we have at least one resident expert on Williams board repairs (RA -- are you out there ?)
There are also some good resources listed in the
Restoration section of the BYOAC wiki, some specific to Williams games.
In the immediate term, you can check all of the connectors to see that they are seated properly (with the power off) -- I've had problems with bad connectors and pins before.
Oh, and definitely take some pics (of the screen and of the innards so that we can see if anything is obviously amiss) and let us know what the code is.