When nothing works, I start at the source(battery, alternator). When some things work like in your case, I pick one item and work from it backward toward the source. Often times running one down and fixing one item will fix a problem that turns out to be common to your other issues.
SO, since it is so vital to other systems, lets start with the alternator... 12/24V power is reaching the PDP otherwise the truck wouldnt start. Exactly what voltage is reaching the 12 and 24V test points on the PDP when setting and with the engine running? Be specific to the decimal... As an example, with fully charged batteries, 12V should be around 12.1-12.3V engine off, and should be around 14.1V with the engine running. 24V should work the same way around 25.2 jumping to around 29V when running.
The alternator does not come online untill the engine is running and has built sufficient oil pressure to turn off the low oil pressure switch and idiot light. Does your low oil pressure light illuminate when you turn on the main switch, and go out shortly after the engine starts and the oil pressure exceeds 15PSI? Alternator excitation is controlled by the same switch that controls the low oil pressure light via a relay. Relay K11. 24V flows from CB77 to pin 30 on K11. When that relay de-energizes once oil pressure is achieved it passes to pin 87A on K11 and on to TL 35 on the alternator to start power generation.
Tilt the cab and check at TL35 on the voltage regulator for 24V with the engine running. If you are getting 24V at TL35 you have a alt or regulator issue or a polarity box issue. A1 polarity box does some switching as well as polarity protection but since you swapped it it is probably not an issue. If no voltage is making it to TL35, you need to look back toward the source of the excitation power(K11 in the PDP).
So, pull relay K11 and with switch on you should see 24V measured to ground from pin 30 in the relay socket(look at the bottom of the relay the pins are labeled). If you have it at pin 30, what is on pin 86? you should also have 24V on that pin and this relay should energize when the main switch is turned on if the pathway from pin 85 to ground thru the oil pressure switch is working. so K11 should energize when you turn on the switch and de-energize when the oil pressure switch opens. If this is working and you had power on pin 30 of K11, you need to confirm the pathway from pin 87A down to TL35 on the regulator. The easiest way to do this is with K11 removed and the engine running, use a jumper wire and jump between pin 30 and pin 87A. If the pathway is intact, you can measure 24V at TL35 and the alternator should come online. If the relay is energizing/de-energizing appropriately and the pathway is OK, then the relay contacts are the issue...
