How do I repair concrete damaged from house settling, on a budget?

Have it looked at by a foundation co and get their ideas. May be more than you can handle

I saw a demo recently and they use a product sold at Home Depot called Sika. Depending on the damage, if it's minor you can do it but extensive damage would be best left to the pros.

Another solution - depending on severity - is to chip out cracks and apply a hydraulic cement.

If it is minor, listen to Kathy, if it is major, most contractors will recommend cutting it out to pour a Truss and a buttress or Just installing a Bilco Door and Entry to the basement.

Pour of a Truss and Buttress is the Easy Part.

Even installing a Bilco Door is the easy part.

The Hard Part is Figuring out the weight dynamics and isoscelean triangulation of exactly where to place the Truss(es) before you knock out a wall.

It is the hard part Because unless this is your hobby or second go at this, (where you just create a Triangle, with 2 Trussess spaced as the Hypotenuse of T=2a+H with H=Square Root of a-squared plus b-Squared, where a=b as an Isoscelean Triangle) you can spend weeks to reproduce a Permenancy of what a Floor Jack femporarily does.

You do not get cracks in a Foundation where trusses or buttresses are properly placed is what I am saying.

Repairing the Crack over and over does not get to the core problem.

Core problem is improper weight distribution.

Did somebody remove the lightweight 1920s Icebox and potbelly coal stove for a 3 ton cabinetry and fridge?

Yeah, Probably...

So...You need to construct at least One Truss [but preferably two, equidistant from the crack and wall you intend to remove and congruent, for both the Trusses] to support any weight that the removed wall won't support, then knock out the wall, then replace that wall with a Wide Buttress or Create an exit with stairs and a Bilco Door.

Not cheap for a Contractor to do, easy talking between $12000 and $22000, reliant on whether they need an architect to advise or oversee. Many do. Some don't. Those that don't , do not necessarily cost less. So if you get a Contractor you Ask they if the have an Architect on the Payroll.

Even If you do it yourself it can run between $2800 to $9000 reliant on the Bilco Door and window and delivery and installation Options and also reliant on if you use stacks of bricks filled with concrete or just concrete for the Trusses and Butress which that creates a bit of another material cost differential too, [seldom only in the hundreds when talking: 24000 lbs of concrete in 300 bags with 1300 bricks and Mortars not less than 420 lbs.].

Aorta problems may result on cost. Expect your eyes to bulge.

Expecting low cost is Sorta like: 'Big Guy in Iittle Shirt'. Sorta.

However, once it is done, you will be done that job for life, for sure.

And never need replace again that part of the foundation nor those trusses.

And if you get a Bilco Door, your life will be much eased too.

All in All, it is worth a 7 grand investment.

Maybe put in a Window too, while you are at it if you got Laundry in the Basement. Not a savings, for sure, but: Good to let out that Dryer and Furnace Humidity in the summer rather than Opening Bilco doors each time you do laundry.