It could also be a "brownout" caused by the voltage "drooping" due to high start-up current of the motor?

It could, and it could be a lot of other things. The bitch about noise is that there is no snakeoil. ANY silly thing can be the cause. I have had experiences with things such as "the system bum out sometimes" finding out that happened when an elevator started. Once I found the cause being noise from scales in a 3 prong humidifier. It can be simple causes, complex causes and who knows what.

The cure for noise is NOT to "fix the problem" but defensive design. If a truly defensively designed circuit bum out you will find that the cause is external such as the one suggested by Andy. If your circuit is designed with no defense against noise, it serves no purpose to hunt outside the board since even correctly functioning devices DO generate noise.

Erik