Who cares if you hide the wires.. all the rest of the wires will be running out the back anyway.. I'd focus on making some sort of connector for them. Glue them in place or come up with some sort of thread and nut socket to hold each one in place. Then fabricate a connector that simply slips over the back end of the led and connects the wires to your voltage source.. which if it's in the computer you can make a little connector that connects to the back of the case.
I'm thinking something like a cable you fabricate out of some old wires from the front of a computer case (LED wires/power button etc.) They'd plug into each led then into the back of the computer (either drill a hole and create a connector (it's just 2 pins sticking out; you can get these black things that hold the 2 pins) or create the connector on the back of a pci slot cover. If they are all going to be powered at the same time your connector would connect one place for power then split off to the 3 different led connectors perhaps.
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