Power needs, motor drivers, and more..

Hey guys,
I'm pretty new to this world of electronics and hardware hacking in general, and I'm working on a project to build a simple 3-wheeled robot that can be controlled over internet.

So far, I was able to get it to work, but not so reliably as I want it to, and I am guessing I have powering issues (or wiring perhaps?).

My setup is as follows:

1. Espruino board
   
2. Adafruit CC3000
   
3. H-Bridge Motor Driver 1A SN754410 (pin-compatible with L293D)
   
4. HC-SR04
   
5. 2x MG-6-48 Gear Motors
   
   

The CC3000, distance sensor and even the motor driver are wired via the breadboard (even thou the Espruino tutorials sort of implied the motor driver goes soldered into the prototyping area).

I have only one power source for everything, either my computer via USB, or a LiPo battery 1400mAh.

If I power it directly via USB with my computer, the whole thing works, but one annoying issue: Usually when I fire a command ("FORWARD", "LEFT", etc), the motors don't really kick in, and I have to literally push it a bit. Once they starts moving, everything keeps on rolling fine.

Now, if I power it via battery, the thing doesn't seem to have power to do anything. Sometimes I have to lift it from the ground for it to start rolling.

So, in summary, my questions are:

1. Is it ok to wire the motor driver via the breadboard instead of the prototyping area, or is this actually a source of trouble?
   
2. Why could it be that even when powered via my computer's USB the are issues to kick in the engines?
   
3. I assume the battery pack I'm using is not enough, right? What's the "proper" solution for this? Buy a battery with higher higher current? Or can I power the motors from one power source (e.g. the 4xAA pack that comes with the kit) and the Espruino with a different one, like the LiPo battery?
   
   

Thanks a bunch in advance, and sorry if some of the questions are extremely dumb! :)

Cheers
gonzalo