hello, well it's difficult without the piece in hands to understand the circuit, and without the schematic, but I could give a try.
1) On a switching PSU, only one output is really stabilized, here it seems 5v. The other outputs are "unregulated", but in some way related to the stabilized one, for example via transformer windings ratio. However, to protect circuits, some voltage range or current range detectors are added, to avoid these outputs to go outside acceptable values. Maybe something in these circuits on secondary section detects a false condition of error, cutting off supply current on primary section. 2) voltage seems to go high too slowly, as if a soft start is going too slow. Normally SS is done charging via a resistor a capacitor on the feedback, affecting maximum current on the primary. If the capacitor is leaking current, it will charge too slowly, and will never reach maximum voltage required, so basically you will never have maximum current in the output. This could be a small capacitor charged by a done kohm resistor. Andrea