Major floor sagging could definitely be a big dollar problem to correct. Correcting it could also crack plaster all over the place. I'd definitely have a structural engineer check it out before going through with a purchase.

The I-Beam is probably a previous owners attempt to fix the structural problem.

If the plaster walls are original, it is quite possible that there is no insulation. The solution to that is to have loose insulation blown in. The cut small holes in the wall, blow the insulation in the empty cavity, and then patch the plaster.

Stone is a lousy insulator. It holds heat very well, but it isn't going to keep the cold out.

I would factor a bunch of things into the equation. One of course is initial cost of the house. Do you plan on staying there long term? (would it be easy to get you investment back if you sold at a later date) Are there benefits to the land that are really important? Are you a handy person?
We bought our house in 1980 for $14,500. It was all we could afford at the time. It's an old mill house built around 1874 of planks and beams without cornerposts. Over the years we've put about $30,000 into it which still isn't bad. We've managed to raise our two kids here. It's on a dead end with a river on one side of the street and woods to hike in, and room for a decent sized garden, 5 beehives, a few out buildings, and hopefully a chicken coop to come, yet it's a 10 minute walk to the center of town. Yes it's fairly rundown and needs more work, but it has character, has the real feeling of home and I wouldn't trade it for any stick built with vinyl siding. We're within 2 grand of being paid off. I will continue to work on it a little at a time, but it's a place with a history and should provide us with warmth, shelter, and memories for the rest of our lives.

Thanks for the replys.

Bill: Is 1.5" across a 10' span considered major floor sagging? I've done a lot of work on newer houses and I know it would be a tremendous problem for a modern structure, but I don't have a feel for what's acceptable in a building of this type. A lot of people post about a little floor sagging is in the nature of these houses... but where does character turn into defect?

The plaster walls certainly seem original. The blown in insulation sounds like a winner. The PO replaced all the windows and doors and when I was in the house the other day I didn't feel any noticable drafts when I put my hands by the windows.

Tony:
I'm 38 and I'd like this to be the house I retire in. The land is very important to me, not just as a place to relax, but as a place for my daughters to play and explore.
I have a degree in electrical engineering, and I used to build custom furniture, mostly case goods; shelves, chests, and cabinetry. I brought my first house back from being condemned (did 90% of the work myself) and my second house only needed new wiring, plumbing and some sheet rock (but those were both modern framed homes). So most work is within my range... but I also know my limits, and major structural work on an old stone farm house is my limits!

Thanks again!

The sagging you describe is hardly anything for a house that age - seriously! It could be SO much worse. The important thing is just to determine what's going on and if its anything out of the ordinary - such as, is it woefully inadequate structurally, is it situated on the edge of a marsh where the ground is not solid. My house has a pretty significant dip in the floor near the chimney because the outer perimeter of the house settled at a different rate as the chimney (which has some joists attached to it) - it probably wont settle anymore but if it does it probably wouldnt be enough to be a problem. An inspector who specializes in old houses should be able to give you all the info you need to make a wise decision - sure you want to be cautious but you don't want to miss out on something fantastic either, you can't really apply new house logic to a house that old. (1850s stone -sigh!! sounds lovely)

The problem with deflection in the middle of a room is that it has nothing to do with settling. If a span slopes in one direction, it is because one side is higher or lower. That is a normal side effect of one area settling more/less than another. If a span slopes toward the middle, it means that the sides are roughly the same height but the joists themselves are bending in the middle. Some deflection across as span is normal and completely safe. Major deflection indicates that something has gone wrong. If 1 room is significantly worse than the others, then it is probably not undersized lumber for the span since the same techniques were likely used throughout the house (unless this is an addition.) It could be a problem they fixed 100 years ago. A previous recent owner could have retro-fitted electrical for a ceiling light by drilling big holes in the middle of the span. Who knows? A lot can happen in 150 years.

IMO - it wouldn't necessarily be a deal breaker. Definitely have it checked out by a pro though - someone with a structural engineering background - not just the first general home inspector you come across.