Test your voltages on the AR-II first. You should have 12-14VDC on the 10.3V test point, and 5V on the + side of C1. It sounds like you have +/-23V on the right side, which are used for the video section of the game board, which generates the XY voltages for the monitor.
If you are missing the 10.3V, you have an issue with your power brick (either a bad bridge rectifier, and/or bad big blue cap, and check all of the fuses).
If you have 10.3V but no 5V, you have an issue with the AR. Look to see if R29 and/or R30 are burnt. If so, you have an issue with your edge connector (which is either dirty, and/or the pins are stretched out and are not making contact with the fingers on the PCB). You can clean the edge connector, repair the pins, and replace the R29 and R30 (both 10 ohms, 1/4 watt).
If the resistors are ok, replace the 2N3055 on the AR. That should get you 5V again. But without 5V, nothing will run, which is why there is no 5V LED lit on the game board.
There is also no need to use a switcher in these, and it's not really straightforward to do anyway, as the AR also provides the audio amplification, so ditching the AR requires separate audio amps. It's just easier to fix the original supply, which is not that hard, and they are perfectly good systems when properly repaired. I can walk you through it, if the above doesn't work.
Be aware you may have other issues, but for any vector game, you want to attack the problem in stages, verifying power, game board, and monitor all separately, one at a time. But it's all doable. Feel free to post any other questions here.