The colors on the leads appear to be insulation, and you twisted them together without stripping them down to bare wires. I wouldn't expect that to work.
If you know how to solder, start by buying a replacement plug designed with a removable cap that will allow you to solder the wires directly to the contacts. You may find one at Radio Shack or any electronics parts store. Be sure you know the outer diameter of the plug. There are 2.5 mm and 3.5 mm plugs that look very similar. If you choose the wrong one, either it will be too big to go into the jack, or it will fit loosely if it's too small.
You'll have three leads, left channel, right channel and common (ground/shield). The blue and red leads are left and right. To keep the channels connected correctly, use an ohm meter to determine which is connected to the tip and which is connected to the ring. You can test which (red or blue) is connected to the tip. The silver (bare) lead is the common/ground/shield connected to the long sleeve part of the plug.
Try to cut the length of the leads beyond the outer insulation just long to reach the contacts comfortably, and strip just enough of the ends of the red and blue wires to connect to their respective contacts.
Don't forget to slide the shell over the wires and down the insulation before you start, and check to see if the plug you buy includes a means of strain relief, possibly a section that crimps around the outer insulation to hold everything inside the shell.
It's an easy job if you don't know how to solder. If you don't, have a friend help you.
Good luck.
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