The A/C on my '98 quit one day (strangely after I had Cummins Atlantic spill-port time the P pump; mere coincidence). The shop I brought it to bypassed the PCM and it has worked since. In my case, the PCM failed to 'turn on' the clutch. My compressor is original (227K miles, 9. 5 years, never serviced), and it works fine. Freon does leak out rather more quickly than I would like, but I expect that, at their age, all the seals and o-rings are pert near shot.
Shop: Mr. Murphy, it looks like you've blown a seal.
Me: Hey! Just fix the darned thing and leave my personal life out of it!
[Adapted from "Wet Dream", album "White Boy Rapp", by Kip Addotta. ]
As I recall, there is +12V feeding the wire that passes through the PCM, the low pressure cutoff switch and the high pressure cuttoff switch on its way to the compressor clutch. If any one of these fails to close the circuit, the A/C won't work. Oh, yeah, first ensure that the PDC is supplying +12V to this circuit!
Unplug the low pressure cutoff switch connector with the engine running and the A/C enabled. You should see +12V on one pin (this is through the PCM) and near ground on the other (this is the clutch side). Not even close to ground? A/C clutch mechanism is the likely culprit. No +12V? PCM is not engaging its relay.
I can almost guarantee that nothing will be harmed if you unplug the low pressure switch connector and apply +12V to the clutch side; for that matter, you could safely apply +12V directly to the correct pin on the clutch for a few moments. If you hear the clutch engage (click), you are on your way to determining the cause of the failure.
One possibility is the low pressure switch has failed; you can remove it, and clean it with a few spritzes of carb cleaner and bang it on a workbench a few times (to bounce the spring and switch). Then make sure all the carb cleaner has evaporated and put it back on. If the A/C now works, buy a new switch, because it probably needs replacing.
The high pressure switch should almost never disengage. Whilst you *can* bypass it, I don't suggest doing so. If the pressure gets too high, you'll hear a loud, discomfitting noise from the compressor. Trust me, I know. Hmmm. I wonder if that's the source of my Freon leak?

More properly, I would expect the system to be filled only to the point where the low pressure side is sucked down far enough to shut off before the high pressure side gets too high.
If you have determined that the circuit to the clutch is good *after* the PCM, you can cut the wire between the PCM and the low pressure switch and run a new wire from the PDC. This is how mine has been set up for 3-4 years now, and it's been working great.
The PCM relay is needed only to allow the PCM to disengage the clutch; typically this happens when climbing a steep grade and the go pedal is matted for a 'long-ish' period. With the mighty Cummins, we never notice when the A/C is running - it's such a low percentage of the engine output - so there's no need for the PCM to control the clutch; it is quite safe to bypass the PCM in this case. But do be sure the high and low pressure cutoff switches are functional; they *are* important.
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