Is it possible for me to short my arduino mega while checking the Vref between the potentiometer and vref pin on a A4988?

My multimeter wasn't picking up a reading, and, when I tried a third time, I noticed my dot matrix screen went off and my computer no longer recognized my device.

I'm thinking I've shorted the voltage regulator.

It's possible, or it may just be that the voltage regulator decided to fail at that point. If your LCD is a 12864 type, then the backlight will draw quite a lot of current and this will probably overheat the voltage regulator on the Arduino.

Modern electronics such as Duet solve both problems. They provide software-adjustable stepper motor current (so no need to mess around with pots and voltmeters), and 5V switching regulators capable of powering LCDs, servos, touch-screen control panels etc.

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Large delta printer [miscsolutions.wordpress.com], E3D tool changer, Robotdigg SCARA printer, Crane Quad and Ormerod

Disclosure: I design Duet electronics and work on RepRapFirmware, [duet3d.com].

its very possible because its hard to hit the right pins one slip and you fried your logic. happened to me twice alread, so i stopped measuring the pods and just adjust them till they feel rigtht