They're not made to be serviceable, though there is a link somewhere online with a guy who did it to his. At the shop I used to work at, the head mechanic showed me how he serviced STI's, and it worked fairly well, but took time; He'd flush everywhere around the lever mechanism internals he could get using WD-40. Then he'd let it sit for a while, come back, flush some more, and start working the lever, over and over. It could take him a few hours, but eventually, he'd get the gunk and springs to loosen up enough, and they'd start working again. I think if you're going to do this, the problem is that the WD-40 is mainly solvent, and after that all evaporates, the internals don't have much grease left inside. Probably good to follow a day later with a dollop or two of thicker oil, like Phil Wood's, that will leave a coat on the little pawls and gears inside the lever. That's assuming you eventually get the thing working again.
PS Here's that link: Read through everything carefully before attempting the actual work.
http://norvil.net/pedal/service/shimanosti/index.php