Why aren't my 4x 612 RPM motors driving with only 12 lb load?

The no load current draw, per motor, is 0.52 amps. You have 4 motors, so you're looking at over 2 amps for no load.

The stall current is TWENTY amps, per motor.

You also appear to not be using an actual battery, but rather some portable power device that has an internal battery. The electronics in it could easily be performing a short circuit detection and killing output to safeguard the battery.

You should check current draw with your multimeter:

1. Make sure the multimeter probes are plugged into the current ("A") connectors, then
2. Make sure the multimeter is set to current, then
3. Attach the positive lead from your battery device to the positive port/probe on the multimeter, then
4. Attach the negative lead from the multimeter to the positive connector on your robot.

You measure current with a multimeter by putting it in series with the load. Putting it between the battery and load will let you measure the total current output of the battery.

I would guess you'll see one of two things:

1. Some small power draw for your electronics, then a rise in current when you try to run the motors, but to an amount not sufficient to run them, like 1 or 1.5 amps, for example, or
2. Some small power draw for your electronics, then suddenly no current at all when you try to run the motors, which would be a short circuit protection disconnecting the power output.

You'll either need more battery packs or you'll need to ditch the portable electronics and use the batteries directly (or both!)

Lastly, your four motors have the potential to draw a combined EIGHTY AMPS of current. I would strongly suggest you check the current limits of the wire gauge you're using, pick a value LESS than that, and add a fuse so you don't start a fire.