I think DAP is the prefix Delta uses for their custom marked chips. Probably you will see “Delta” or the the Delta logo somewhere else on the board. In that case, those ICs are going to be pretty much impossible to replace. I have not seen too many FETs blow open circuit, so I would not imagine FET is actually shot in that case.
Also, didn’t read your post very closely before, but since it is producing output voltage, this is pretty much rules out dead MOSFET. What is the power rating? Photo of the top and bottom side of the board?
Could be many things, but one idea is to check the VCC capacitor, usually small electrolytic on the primary side. At no load, the MOSFET gate drivers average current requirement is not that high (usually operating in skip/burst mode). At higher loads, gate drive energy requirement is higher, so could explain why the output drops out under load.
Could also just be bad feedback loop component.