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My LBS tried to bleed it, couldn't, and gave it back to me. They came to the same conclusion that I initially did, that something was broken inside the shifter so this forum has been much more helpful!
I actually bled it yesterday and rode it today, had a few issues with the bleed (pushing the lever all the way in, when opening and closing the caliper bleed nipple for example, seems to block the shifter up again) but I managed it and seems all good now :)
Bring it to your LBS with a 6 pack in hand and ask if they'll have a look at it, you'll probably have to pay for their time too but the beers make things go faster!