I had a board that overheated come back to life when I let it rest for like a day, so trying again later might help...
Did you check the resistance between the voltages before you wired it up? As to check that there are no shorts / that the sides have been sanded fine enough?
Btw you only need one ground wire and one 3.3v wire, they are internally connected, though I don't think it will make any difference between having multiple.
Haven't see any shorts immediately from the pictures, maybe the look at the backside of the wii?
Or again maybe the sides have not been sanded fine enough? If it booted and worked for a while, it might not be a direct short, but rather the resistance that is too low so that it consumed more power than intended?
Also, from what I have gathered on this forum, I think the cpu is what produces the most heat, so the small heatsink on it is probably not enough to run for any significant time. This is just conjecture, but if the wii overheated first and failed, it might have overdrawn power from the pms causing it to fail afterward?
Also, check the battery voltage, if it ran for a while they might just be low, causing the pms to not power on due to low voltage?