Thanks Smith & Sbampato for suggestions.
Smith - I have inspected the board closely and don't see any obvious solder issues. Almost all the caps on the board are surface mount ceramics, so I think unlikely to be an issue. I will check out the two electrolytics. I have the sense that the large one is doing its job in the power supply, as the wave form downstream of it and into the voltage regulator looks smoothed. As both you and Sbampato have suggested, there could still be some ugliness on the power supply. I suppose that one way to explore this would be to just bypass the power section and feed a known, good 5V after the regulator and see if it powers up. I didn't mention it above, but I live in Madagascar, and the power grid here is pretty hard on the front end of power supplies.
Sbampato - When the unit does power up, it works correctly. Given that, I don't think there is a problem with memory corruption. As far as I know, the triac is working correctly. Are you suggesting that the triac could somehow affect the digital section of the board? I will look more into the 5V rail, as above.
Thanks,
Jack