Hi!
So you used the GameCube it's power supply on the Wii U?
The worst case is that your Wii U took damage or the power supply.
I would try a new power supply and see if this fixes it for your GameCube!!
If not, then you probably need to inspect the motherboard and check the caps.
Also check the power board and replace if needed.
Part: https://www.ebay.co.uk/itm/194935186310?chn=ps&_ul=GB&norover=1&mkevt=1&mkrid=710-169684-531343-4&mkcid=2&itemid=194935186310&targetid=325425753764&device=c&mktype=pla&googleloc=9193247&poi=&campaignid=20649934318&mkgroupid=153764631759&rlsatarget=pla-325425753764&abcId=&merchantid=431263316&gad_source=1&gclid=EAIaIQobChMIwv7XrqKkiAMV0EdBAh07dAK_EAQYEyABEgK6f_D_BwE
Please let us know how it goes!