Ok you have a very basic breakout board there, it looks like it has numbers on it and those will likely be the pin numbers you put in Mach. The Gecko drives have Step/Dir markings on them so you can trace the wires from them and you will know which pin is Step and which pin is Dir for each axis.
Hood

I traced out the RS-232 and the path is as most say, and I have tried several times (i.e., x step 2, x dir 3, y step 4, y dir 5, z step 6, z dir 7).  Pin 15 has a grey wire that goes to the 2-pin molex plug on the cabinet and the other pin of the 2 pin molex plug goes to the RS232 ground.  No where do I see a ground between the gecko drives and the RS-232 port.  The port marked "Common" on the Gecko drives are conneted in parallel and exit through the 2 pin (but only 1 pin present) molex plug labled "5 volts."  The 4 pin molex plug goes to the RS-232 ports 10, 12, and 13 and nowhere else.  The other molex plugs are empty.

Is there anything I should be looking at to trouble shoot the system from here (e.g., motor wiring or Gecko setting)?

Thanks

Ok the Geckos require a 5v common so you need to connect that to a 5v supply, possibly take a USB cable and chop the end off and connect the red wire to that molex labeled 5v.
The other molex with the one grey  is likely meant to be for an E-Stop switch.
Hood

Thanks.  That explains a lot.

At one point JT said that there should be a molex cable for the 5 volts.  It sure would have been nice to have the manual.  I don't suppose that there is any pin along the RS-232 to tap the 5 volts from?

You could take a molex from your computers power supply to it, Red wire on the 4 pin molex that connects to IDE Hard drives is the 5v.

Hood

Now your cooking with gas.
Looks like two transformers to proivde total amperage and voltage. Go to the Gecko site and download info on the drives.
Check the size  resistors  across the two current set terminals ( actualy it's on the case). Too high a current setting and you will burn out your steppers ( they will get hot quickly), to low and they will not run. Trace each wire to make sure they are correctly run from the drive to the stepper for how the stepper is wired.  Never disconnect the drive when the motors are energized ( you'll blow the drive). Keep the caps on the drives. You should see the light glow red if the drive is working. Check the fuses
to see what amp rating they are as compared to the amp setting on the drive.

RICH

It looks like nobody fooled with the contoller  but you do need a 5v common so you need to connect that to a 5v supply as Hood said.
BTW, I installed switch's which  takes out the 5 volts to the all or any of the drives and thus it will imeadiately stop each or all of the motors. 

Now post your xml file.
RICH

OK, when I turn on my computer, I get 5.02 volts on several pins of the DB25 cable including Pins 11, 12, and 13, none of which are being used to operate the machine.  Can't I simply cut the wire off the molex plug that goes to the Gecko common and wire it to Pin 11 so that everytime the computer powers up, it sees the 5 volts?

It seems like the easiest solution and there would be ne need for a separate cable.

I dont think you will have enough current there.
Hood

Can it hurt anything to try?

Thanks