Hi Cazkade, tricky to know what's going here, could be lots of things.
The biggest problem I ever came across with the L293D-based shield was that the motors, the power supply needed to be very closely matched to the L293D's capabilities - nothing is adjustable.
"Powering down" happens when the machine has been inactive for a set length of time (600,000ms = 10 minutes - see the code here https://github.com/euphy/polargraph_server_a1/blob/master/impl_uno.ino#L90-L99). That's designed to stop the machine from overheating and burning out driver chips. Holding the motors still, but at full power causes them to heat up, which lowers resistance, which allows more current to flow, which causes them to heat up, and so on. There's often a whining noise when the motors are held still and the whining changes frequency as the motor gets hotter.
The chips from the motorshield _can_ get fried, they can overheat. There is no thermal protection built into them. I think I'd be surprised if that caused the arduino itself to be damaged though, if it was wired up without the EXT_PWR jumper on the motor shield.
1. Does your arduino error happen when you have the bare arduino connected via USB? I mean, without having the motorshield attached? What error do you get?
2. Did the "Powering off" message happen after a long period of inactivity?
3. Which motors do you have?
4. Did you solder the piggy-backed L293Ds onto the ones below, or are they just push-fit?