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you wanna ghetto rig it?
strip the end of the wires that come with the inverter, shove them carefully into the 12v and gnd of one of your molex's from your computer PSU, tape it up with some electrical tape and it'll stay on while you're computer is on..
now if you want to add a switch.. thats different
wire the switch into the equation and use elec tape and wires twisted where you'd normally solder and use heatshrink.
..that's how id do it. 
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pick up one of these
3 to 4 pin adapter
connect the wires from cathode to the inverter an you should have 2 bare wires coming off the inverter.
Strip off the 3 pinned molex leaving 2 bare wires.
Match the colors, twist and wrap around with electrical tape.
simply plug in the 4 pin the powersupply.
Takes about 10 minutes!
Turn on the computer and enjoy!!! using an adapter avoids having to splice up your valuable powersupply wires.