Hmmm, with the Arduino powered from USB the Motor shield 5V should be coming from the Arduino, not the motor supply - its unclear whether that shield has its own 5V regulator (datasheet for the shield is important imformation).
I suspect the problem is somehow a lot of current is being pulled from the Arduino 5V pin causing the computer USB power chip to panic and shut down.
L293's and L298's have the woeful behaviour of internal phantom powering of the motor rail from the 5V rail if 5V is applied and Vm isn't present - this will lead to excessive current draw and possible damage to the chip even.
So you have to ensure Vm is present before 5V is applied to prevent this internal phantom powering happening.
If Vm was to come from a small 9V alkaline battery this is incapable of powering 4 motors and would immediate overload and drop below 5V, causing the internal phantom powering mode and then perhaps overloading the USB?