First and foremost my condolences to you and your family on your loss. 🙏

Sometimes the simplest item is the answer. Sometimes.

There are 4 wheel speed sensors (one at each wheel) that are connected directly to the ABS Controller. I would suggest you try to narrow down which one is showing the erroneous reading and start checking from there.

 

I suspect is an incorrect speed reading if all passes until the car starts moving, especially since it being an AWD just like AUTOMATICs, there are 5 speed sensors. 4 wheel speed and one transmission shaft speed.
For it to trip the light so quickly I'm willing to bet is one of your wheel speeds.

 

I’m looking at buying a 2009 g37x and when I test drive it the AWd light was on the whole time. Should I be worried or buy it. $4000 with 136,000

 

That depends... if you want rear wheel drive, buy it.... If you want "all wheel drive" don't buy it.

 

I agree with Sonic, a first gen G37 AWD at 136k miles with an AWD trouble code is nothing but trouble + a ton of maintenance. You should be able to find something better for that price.