Welp, the other day I got a new analog board. Recapped the three RIFAs, the seller said it was taken from a working mac, and guess what? It still has the same issue! I really have no idea.... could it be a CRT issue? Maybe the CRT has weird current draws or has issues, I don't know. Really stuck!
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It’s pretty much a given that since you’ve swapped the analog board and the symptoms haven't changed at all, the trouble is likely living on the logic board. You can definitely stop worrying about those RIFAs for now. They’re just there to filter RF noise on the AC lines and won't actually stop the machine from booting or cause logic issues.
The great news is that you're getting a boot chime! That’s a huge win because it means your CPU is alive, running code, and successfully talking to the ROMs. Since we can probably rule out the analog board, here’s where I’d focus your energy on the logic board to stop that chime loop.
Since you're testing without the case, we know the plastic buttons aren't physically stuck, but the circuit itself could still be latching low. On the Mac Plus, the Reset and Interrupt lines are "open collector," meaning multiple things can pull them to ground to trigger a restart.
Even without the external switch, the physical push-buttons on the board can internally short or get gunked up with debris, making them trigger with the slightest vibration.
It’s worth checking the continuity on those switches or even using a logic probe to see if the HALT or RESET pins on the 68000 are pulsing low when they shouldn't be. If a buffer chip in that path has failed, it might be holding the CPU in a permanent reboot cycle.