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I think a little sleuthing will reveal a bad relay coil. Take your AC relay and plug that in and try it

I would pull it and have it checked

But, does it work now?

Does the starter work?

Symptoms?

Basically, the NSS provides a ground to the starter relay in the PCM. Even on the late models with the AW4. The easy way to bypass the NSS is to just permanently ground the wire from the starter...

As long as the oil doesn't leak out, no

No, bypassing it does not hurt it. Other trannys it might, such as the 45RFE in the WJ, but it would end up being a computer thing. The AW4 is not that sophisticated. I have a different trans, but...

If you got it to start by supplying power to the starter relay, then yes you are probably on the right track with the NSS. The consensus is they can be cleaned and work again. But as you found out,...