... Certainly not the kind of job I'd personally be interested in undertaking! As Bruce and Don say, it's just the kind of job you really don't want to do. If you really need to be convinced, have 3 contractors come out and estimate the job. I bet 2 of them won't do it and the 3rd will charge you the price of a new home. Yes, it's discouraging but that's really the jist of what everyone is saying.
However, there are a couple of options so hope is not totally lost. As mentioned in another follow-up, you could look into putting in skylites. We have a 1-story addition where 1/2 of it is an extension of our kitchen. The addition is on the north side of the house too. (The 2nd half of the addition is the family room.) Besides being on the north side, the 2nd story of the main house 'blocks' out what little light there is to get to the back of the house especially from late Fall to early Spring. We eat in the 'addition' part of the kitchen. When I re-did the roof of the addition last Summer, I had someone come in and put in a nice Velux Skylite. W/O the skylight, it would be pretty gloom in a room that's suppose to be warm and bright. The roof of the addition slopes away, towards the north. The highest point of the roof on the addition is about 5' over a distance of 15'. This is actually considered a low pitch roof. I'll spare the special precautions we did to prevent leaks, ice damning, and the transport of run-off (because that's not what you're asking here.) What I want to mention about the skylite is that, (since our roof is pitched; not flat), the 'lower' end of the skylite is about 3' up from the ceiling and the 'high' end of the skylite is about 5' up from the ceiling. In short, it's recessed 'up there' and, of course, since the roof is pitched, the skylight is pitched too. You might ask, "How do you get light into the eating area if it's recessed so far into the ceiling/roof? How does natural light make it to the floor?" Well, the 'cavity' that the skylite is set in is drywall that's painted white. Our kitchen walls, however, are a light cream. To put it another way, we needed all the 'help' we could get to have what little light there was, make its way into the kitchen! Light colored everything, from walls to cabinets to flooring, is what we did. All this, of course, is to handle our unique living situation. YOUR situation, like ours, is unique too. Just consider these types of things when you do the job (high sun, low sun, path of sun through skylites year-round, heat trapping/ventilation, UV, color of walls et al., furniture fading, tempered vs. non-tempered, etc., etc.)
Now for the good stuff you've been waiting for. Veluxis just one company that sells skylights. They're a bit expensive when you're putting in a few skylights. But if you're putting in 2 or 3, they're worth looking into because they're good quality. Another option is what are called Tunnel Lites. Atlite Skylights and SunTunnel are 2 sites that market this kind of product. They've been around for a few years in the Home Centers. If you can't find them, contact the manufactures or a General Contractor. With any luck, you'll find a solution to your problem(s) w/o having to raise the roof.
Good luck. If you have any further questions, post 'em up or e-mail me directly.