Logic probes are ok, but an o'scope will show you so much more. They are not that hard to use, plenty of online tutorials, and some great bargins can be had on used units on ebay.

One easy way to use one, is to go through a known good board, taking pics of pertinent signals on the display, then compare to the board giving you trouble.

Also, o'scopes can be a valuable tool troubleshooting power supply boards. DC,AC, and ripple can allbe easily observed.

I have a Tektronics 2330 that Ipicked up for around $100. At 100mhz, it's a little overkill
For pinball use, but the dual trace feature is nice.plus, it has the built in DMM in the lid. It's the same one I used for years when I was in the USN, so I'm very familiar with it.