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First, try this. Turn the key all the way to the ON or RUN position, and within 3 seconds tap that button once. This should disarm the alarm, quiet the siren and allow you to start.
If this fails to work, you'll need to bypass the starter kill portion and remove power from the system.
I'll try to be as descriptive as I can, without getting too technical on you. You will need to remove the panel that is located underneath the steering wheel. There will be a bolt (10mm) to the left bottom corner, and either a bolt or a screw on the bottom right hand corner. Now remove the pocket on the left side, and I believe there is a screw up in the top of it. (this screw may or may not be there, i'm going from memory here).
Now the panel is only held in with clips, so you can grab it and give it a sharp tug and it should come out. This will expose a large wire harness going up towards the steering wheel. Somewhere in this area you will see where a lot of wires are connected to this harness (As well as others) that just don't look like they belong. You want to disconnect all wires going to the ignition key switch (where you put the key in to start the car). There are a lot of big wires behind this switch that will be connected to, and these are the ones we are concerned with. There should be 2 wires either spliced in to, or with a scotch lock style connector. Disconnect both of these. One wire will be cut, with each side of that wire connected to wires that don't belong, leading to a small box (relay). This is what disconnects the starter. You will want to reconnect these wires back together and use a butt connector or solder this wire back together.
Now the vehicle should be able to start. At this point I would recommend taking it up to a professional to complete the removal entirely, and ensure that your starter wire is securely connected to prevent future problems.