Hi Levi!
Yes, those 3300uf 6.3V caps are known to fail.
Good thing you replaced those!
How is the Clock capacitor? Still OK? You could replace this one as well and clean the whole board.
Anyway, the PSU is likely to fail (soldering is getting bad near the power plug), please check those solder joints.
Otherwise you need to replace the PSU for a new one and see how that goes. But, before doing this, are you sure that there are no solder splashes on the motherboard? It could cause a short and thus prevent the console from turning on. Please check this as well. If it's all fine and if there are no shorts, try a new PSU and see how that goes.
If you have any more questions, please let us know!