I’d start by taking all the sid chips out to be safe…
Does the LCD light up and/or show characters? how about the LEDs?
Does the regulator get hot? can you measure the voltage at the regulator and see if it drops out when the core reboots? Are the elko caps in the right way?
Do you get any midi messages or sound?
It sounds like a brownout reset, or maybe overheating (which could be a short).
I would suspect the power supply. I had issues with a box I built a while ago, It would work fine, and when I lit a certain amount of leds, it would reboot. Interesting thing was, some outlets would work fine and others it would reboot. So I know this indicates weird power in the house, but I think it was more that the PS was very crappy and sensitive, I got a higher quality one and the problem totally went away.
I have not mesured anything yet. But i might have found the issue. I think a crystal is shorting out. (time to insert the protectors and then look further.)
Thanks so far everyone i will update when i have adressed this issue.