Wolf36! Thanks for the good word! We have changed the name to Lighthouse LEDs from Niktronix, but it is still the same people and same products behind the scenes. Anyways, enough of that and to the question of the OP. I would recommend using the 12v on the dvd drive too. You will have to carefully splice into the wires as described by wolf36. Then once you do that you need to take a ground wire and a 12v wire from the dvd drive. After that you should prep your leds. The only way to safely do it without resistors is to use them in series (red, yellow, orange you will need 6 and all other colors 4 in series will do).
Here is how to hook them up in series. Take a single led and then connect the positive leg to another one of the leds negative legs, then take the newly connected led's positive leg and connect it to a new led's negative leg and so on. A picture is worth a thousand words here (quick google will result in hundreds of photos). Then when you are at the end of your string, one end will have a + and the other a -. Just connect the appropriate ground and 12v wires and they will safely light.
Best of luck and post up some photos!!
You definitely should invest in a solder iron and solder for a few $$'s if you intend on doing any more mods. Once you learn to solder (very easy for this type of stuff) then you will feel unstoppable with leds. lol.