Please post the markings on the integrated circuit packages themselves. The WT7502 is an IC that I am not immediately familiar with, but I understand the general function and and necessity of a supervisor. Since it is on the "output side" of the converter and, as you say, monitors the V33, V5 nodes it is in part responsible to make sure that if an over voltage occurs on one of the monitored output rails +5V, +3.3V, maybe also +12V rails if it monitors any/all of those directly, etc. does not result in the PSU continuing to perpetuate that problem. So typically such a supervisor will shut down the PSU somehow if there is overvoltage. Maybe also over current and under voltage could be additional failures detected. There is usually some time limit over which the conditions are monitored and a fault condition is decided if the out of bounds reading exists for more than the threshold time.
Your point in mentioning that IC is a good one in that if the PSU was ordered to shut down, or be in the "off" state it would possibly exhibit symptoms like you describe. So yes, make sure the "soft on" wire that controls whether the PSU should be "on" or in stand by is correct and in the state it should be to activate the PSU.
PSUs usually require a minimum load on some of their primary output rails for proper regulation to occur. Sometimes they even shut down or malfunction if a minimum load is not present on some rails like maybe one of the +12V and maybe also +5V and +3.3V, depends on the PSU. So if you do not already have a "dummy load" attached while testing, see if you can hook up some power resistors or a motherboard or something that is safe to test with.
I don't know how the power supervisor IC(s) shut down the PSU. There will be three converters at least, the AC mains side PFC boost, the AC mains side bridge or other type of converter that convets +350VDC to +12VDC and other outputs somehow, and the +5V standby converter you mentioned was working.
There must be high isolation from the AC mains / +350VDC side of the PSU and the +12V / other low voltage side of the PSU. So only circuits like optocouplers or transformers should exist to connect signals other than earth GND between the hot side and low voltage side of the PSU. So somewhere the "shutdown" signal from the "soft on/off" power supply activation wire as well as the shutdown signal from the voltage supervisor(s) must cross the isolation boundary by optocoupler or similar.
Anyway ultimately the full bridge converter IC must have a "start / stop" control and also the PFC boost converter must have a start/stop control. They will be "off" when the PSU is "soft off" or in a fault condition (I am assuming that also applies to the PFC DC-DC boost converter system).
When I say converter I mean either generally a whole block of circuitry that does a particular kind of conversion function like the standby flyback ACDC converter, the main full bridge DCDC converter, or the DCDC PFC boost converter systems. Each of those will have a transformer, some FETs, diodes, capacitors associated with them and also one of more integrated circuits ICs usually from 4 pins to maybe around 24 pins in size as well as smaller 3 pin transistors or whatever.
Anyway identify the PFC boost converter section's control IC which should be near the AC mains input, the associated rectifiers, and the 400VDC capacitor bank and it should be a smaller / simpler IC than the main DCDC bridge converter control IC.
Get the data sheet download for the ICs that are supervisors or optocouplers or DCDC converter controller / regulator ICs. And then check to see if the "enable" or "fault" or other such control lines of then are in the expected state.
If you have an oscilloscope and can safely monitor the PSU during operations (it takes special safety procedures needless to say) then you can also see if you see any activity of the "enable" or "shutdown" or similar lines when the PSU is first plugged into the mains. Sometimes PSUs with faults will actually try to start up for maybe a fraction of a second and then they will stop if they detect a fault.
I suppose with an advanced PSU the detected fault could even be something like the fan not spinning but my intuition has to do with another kind of control line or supervision or PFC boost circuit fault so far.
By converter, do you mean transformer? If so, the main "transformer/converter" is a "Viking E216944-W H-P CWT 1209", for which I am unable to find any datasheet. Transformer has 6 terminals on the primary side and 8 terminals on the secondary side (DC side).
You mentioned an "IC" chip that brought this to mind:
I did look into WT7502 ("PC Power Supply Supervisor"). My understanding is that it looks for the correct voltages on input terminals before it will initiate power to actually turn the PSU on. NOTE I MIGHT BE MISUNDERSTANDING THIS COMPONENT. The green wire (on/off) that switches the power supply on and off connects to terminal 4 of the Supervisor. I also checked and did not find voltage on either V33, V5 or VSS (all input signals) to this Supervisor. I assumed the lack of input voltages is preventing the "Supervisor" from pushing power to the transformer/converter (Viking E216944 previously mentioned) so, I turned my search elsewhere for now. Kinda hard to suspect this supervisor as it is situated near the 12vDC output (to peripherals). If you can see the top view photo it is located just between where the blue (-12v) and black wires go into the board at the bottom-left of the photo. I assumed I was way off and moved closer to the primary side of the main looking for voltage to transform for the secondary side.
I am puzzled by how I am getting DC readings before the main transformer actually "transforms" the 60hz wave into DC for the secondary side. [scratching head]. Sorry, I am trying to swallow all of this as quickly as I can and will put some more research into what you said in the morning.
I greatly appreciate your food for thought on this; thank you for taking the time to respond.