Time Capsule Won't Power on, PS seems good

Not good ;-{

You could try disconnecting the drive to see if that is clamping the power (shorted out), otherwise you have a logic board issue which will be hard to diagnose as there are no publicly available schematics or board views to reference.

Triple check all the flex cables - either you may have not connected them well enough or some of them may have torn accidentally - if possible check their continuity with a multimeter and some really thin probes.

P.S.: I’d even start with checking if the power socket wires are soldered as they should after reassembly and if they are still continuous - if not this could be an easy fix