Replacing 5 V pin with battery not working
Your coin cells have far too little peak current capacity to run anything but the tiniest sort of motor.  As a result the voltage is probably much lower under load.  Your L293D being a bipolar bridge will also have very high loss - probably in excess of a 1-volt drop by the time you count both top and bottom switches.  

Further, your develoment board may not be designed to handle the (lightly loaded) voltage of two coins cells in series, so you may have already damaged it.

If you want an "easy" way to replace a 5v supply with a battery, you might consider using a USB powerbank, though they can have various sorts of turn-on behavior and some may turn themselves off below a minimum current draw.  Doing it yourself is likely to either require a number of AA cells to get well above the target voltage even at end-of life, followed by a linear regulator.  Or better your can use switching regulator or potentially a boost converter from a lower battery voltage (which incidentally is what a USB power bank is - some buck regulate from 2 lithium cells, others boost from 1, both typically cells good for well over an amp).