I have seen systems going into watchdog reset when another device was switched on/off because the code could not handle "silly" input from EMI.
Are you using a supervisor chip, a RC reset WILL fail on occasion.
I am much more inclined to think the problem is grounding than power, what is your uC device connected to as input or output.
such as a 300W computer are you sure it is "such as" not "the", please tell which other devices makes it happen.

Erik