L293D DC motor affecting LCD display
You're suffering from really bad ground loops.  Basically, you've carefully arranged things so that all of the hash that the motor generates is forced to travel through a ground wire that should be providing a nice 0V reference to all of the digital bits.  This means that one thing's ground is not another thing's ground.

Draw a dotted line through the schematic.  On one side, put the motor, battery, and driver.  On the other side, put all the sensitive digital stuff.  Connect the motor-side and digital-side ground at exactly one point on the schematic.  Connect the motor-side and digital-side +12V at exactly one point on the schematic (the suggested choke isn't a bad idea, but it may not be necessary -- getting the wiring right is).

Now connect your circuit the same way.  One point on ground that is common to both circuits; one point on +12V that is common to both circuits.  No possible path for the motor current to flow back to the battery that includes the processor, clock, or display.

See if that helps.