I'd poersonally recommend re-reading the economy boa5rd tutorials. The new Saber Buiklder board you're using wires almost exactle the same as the old style boards - you just treat the single LED negative as you would the three negatives on the old boards.
That said, you've got this wired up funny, and you're missing an important piece. I'm taking a few minutes to edit one of the tutorials to mimic my setup and suit your own.
Lose the buckpuck - it's only working now because the batteries put out about 5v fresh. After a little while, the combined voltage will settle to 4.5v and then lower when they start dying. That won't be enough to power the puck.
Also lose the latching switch you have hooked into the battery pack. I assume it's there because you couldn't get the puck powered off the board. We're going to fix that.
The imporant piece you're missing is a TIP42C transistor, which you can pick up at Radio Shack. This lets you read the LED signal from the board, but power the LEDs straight off the battery. As drawn above, left pin goes to board-LED negative, center pin goes to the actual LED positive lines, and right pin goes to battery positive. Your actual LED negatives go back to the battery pack.
The little bubble switch that came with the saber to turn it on and off will still work, but if you want to replace it with something else, you can pick up a momentary switch at Radio Shack.
Without the buckpuck, you'll need a resistor between your transistor and the LEDs (which I assume are wired in parallel). I'm checking your other thread, it looks like you're using 3v, 20mA LEDs. Your options are:
A) (x40-50) 82ohm 1/8W resistors, one per LED
B1) A singular 2.2ohm, 1.4W+ resistor if powering 40 LEDs (3v @ 800mA)
B2) A singular 1.5ohm, 1.5W+ resistor if powering 50 LEDs (3v @ 1000mA)
If you can't find 1.5W resistors at Radio shack, step up to the next value, probably 2-5W. It's fine to go higher here, it just means a physically larger resistor you have to stuff into the hilt. Just be sure to match the ohms.