Adding pin numbers means you consulting someone else and therefore have made concluions from information not requested. That causes confusion. Adding to what I asked for only confused issues. Forget everything you provided to learn from what is provided below. Forget everything except what you saw on any one red, orange, yellow, green, gray and purple wire. And what you answered concerning the speaker. Now appreciate the massive - so much - information that came only from those requested voltages.
The power supply controller is ordering the CPU to execute. So finally we have accomplished only one thing. We know the power supply system is 100% (definitively) good. Only now can we move on to other suspects - and never look back.
What you saw from those numbers: when the power switch was pressed, green wire ordered the power supply to power on. The power supply sees all critical voltages obtain minimum values. Then we confirmed those value are sufficiently above what is required. Power supply tells the controller (via gray wire) to let the CPU start working. Entire power supply system is 100% good.
According to those numbers, your system is not consumed any significant power.
Next, CPU only looks at a very few system functions. It reads a first instruction from the BIOS to start setting up other functions. IOW you could remove all disk drives, sound cards, network cards, keyboard, mouse, etc and the CPU does not care.
The CPU starts by viewing only a few items, putting letters on the video (using the most primitive video functions), and announcing problems with speaker beeps. One of the first things checked is memory. If memory is not seen, then CPU beeps the speaker. Simply remove only memory boards. If CPU executes and if speaker is working, the CPU beeps that speaker using almost zero hardware. But CPU does not execute; it does not even beep the speaker.
( BTW: speaker – not the soundcard speaker. Soundcard is just as irrelevant as the mouse and disk drives. A tiny speaker on the motherboard that only beeps.)
No letters on the video. No speaker beeps. Now the numbers of suspects has been reduced from so many hundreds to maybe only 20. (Not even on the list of many hundreds suspects is disk drive, keyboard, etc - discussed later). Very few functions are necessary for a CPU to execute and beep the speaker. So now we have limited failure to maybe twenty suspects; and all are on the motherboard.
I assume you have connected the power connector near the CPU. Failure is probably in a tiny area of motherboard near CPU and adjacent large support chips - also called the Northbridge and Southbridge.
A failure that is visible almost never exists. But it is all you have left to inspect without far more advanced equipment. Inspect for stray metal fragments or anything that might short the motherboard in a region around the CPU and those large support chips. Carefully remove the motherboard looking for something (such as a metal standoff) that might have broken through a green coated solder trace. Maybe inspect for a cracked trace or some other mechanical defect in that area.
All but the rarest defect are not visible. We have reduced the defect area only to components in a small area of the motherboard. If the defect is not visual, you have no alternative but to replace the motherboard.
If I was to bet on a suspect (if I was a Roulette player), I would bet on a total failure of the CPU power supply - a function powered by the four (or six) pin connector near the CPU. That failure means a motherboard replacement.
You made analysis far more difficult by discussing things such as the keyboard lights. Keyboard, disk drives, etc all separate computers. Those computers do nothing to impede the main (motherboard) computer. Their actions mean nothing because the meter reported the only important fact.
The fact that the speaker did not beep means the CPU (or an adjacent function) is not operating.
Now, for that pci status board. Hopefully you always disconnected the AC power cord before installing or removing that board. Go back to what you saw on the purple wire. It was always 5 volts both before and after power switch was pressed. If you installed or removed anything when that purple wire had power, then you might have causes hardware damage. That caution even applies to the PCI status board. Always disconnect power cord before installing or removing any computer part or peripheral card. Another thing learned from those multimeter voltages.
Assuming the PCI status board is working, it would have posted some numbers as soon as the CPU starting executing. No numbers? Either that board was defective or it confirms what the speaker reported - CPU was never executing even after told to do so by the power supply controller.
Maybe search the internet for others whose HP Pavilion a6437c was disassembled in the computer junk yard - get that used motherboard.
Appreciate how much information was only in those six voltages (and why all that other information only made learning even more difficult). It took almost forever to get useful numbers. Excessively complicated by reading what others posted, listing pin numbers (which only confused everything), providing other useless voltages, discussing fan and describing keyboard and disk drive lights.
Also notice a fast analysis by disconnecting nothing until the very end (and then only the memory boards).