Disassembling Shimano integrated gear shifters (brifters)
It took me 4 hours but I managed to disassemble the shifter and fix the problem. The cause was a broken spring inside the shifter. I replaced the spring, put it all back together and now its working fine.

Here's a rough description on how to disassemble the shifter:


Release the brake cable
Release the gear cable
Stick a 5mm allen wrench under the rubber cover on the outside of the shifter. You'll find a screw there. Unscrew it and pull the shifter back to remove it
Remove the brake cable pivot pin inside the shifter
Pulling the brake will reveal the screws inside the shifter. Unscrew them one by one
At this point you should be able to remove the plastic housing
Unscrew the big screw at the center of the shifter (it is the screw that holds the whole cog/lever system together)
Don't make the same mistake as me and make sure to hold the shifter together while you undo the screw, otherwise the whole thing will explode into a lot of small cogs, springs etc on your floor.


As other people here said, the hard part is putting it back together so try to do your best to memorize where each thing goes as you take them off one by one. Also try the method described by mattnz first, if it works you'll be saved a lot of hassle.

Hope this will be of some help to somebody.