my collection a while back I was only able to test this out after
getting another SC3000H with a known working PSU. After finding
it wouldn't power up I opened it up to discover that the solder
joins between the power switch and the motherboard and come apart.
In the end
the fix was fairly simple, I heated the existing solder on the
pins and joined them together again. After doing this the Sega
SC3000H started up fine.
As I also
have another Sega SC3000 with the same problem I suspect that
this issue could be common with these computers, it would seem
to happen because of the way the power switch is connected to
the motherboard. Any movement of the switch, which is going to
happen with a power switch will eventually weaken the solder joins
to the point where they break apart.