Power is a problem for most starting out in hobby robotics. I will assume you are using 6 AA alkaline batteries for everything and the you have it running to the L293 and to the Uno as well. I will also assume you are not powering the L293 from the Uno.
Now...
The L293, though cheap, is a very power stealing H-bridge. The voltage drop is quite high vs newer controllers like the L9110 and many others.
Alkaline or Super Duty batteries are also a poor choices for a bot, especially a 4wd bot. They will not deliver the power you need, or if they do, not for very long. NiMH or even NiCad rechargeables would be a better choice. 5 of them should power the motors fine.
I would also power the Arduino and motors with separate battery packs if you can. Just remember to have a common ground ref between the two.
4WD bots are also a pain to get moving, especially with the little yellow gear motors or other low torque motors. I usually ramp up the motors to the speed I want to drive at. This helps eliminate spin-out and gains max torque faster. You can do this by dividing up your max speed by say 4, and in a loop add that quotient to the speed and do a analogWrite with it on each iteration. At the end of the loop, do a final write of the max speed you wanted.