Thanks for all the replies. That $2900 figure seemed awfully high. I'll do some more research, and get more bids.
GregL, what you're talking about is mud-jacking. And, if these sidewalk slabs weren't right up against a basement wall, that's what I'd do. They just drill a small hole or two and pump in whatever it is they use.
Put that up against a basement wall, though, and it puts more pressure on it. Bear in mind that we had all this work done to reduce the amount of water we were getting into the basement because of the wall problems. "Whitey" replaced most of the blocks going down to the foundation because the wall was buckled.
What "Whitey" (if I ever see that MF again, his new nickname will be "Black and Blue") did was to tear the wall down to the foundation, and rebuild it.
That's what I told him to do.
He didn't tell me that there was no drain tile around that portion of the basement. No drain tile=no drainage=water in the basement.
Barbara: once again, you're my shining angel. Next year, the city is going to tear up our streets (and my front yard) to put in a new street and sewer system. All of the work will be done by private contactors. I'm just guessing that those private contractors--or even one of the workmen--would be willing to do some "side" jobs.
Now I just have to figure out how to get those guys to rebuild my chimney for less than the $8,000 I've been quoted so far.
If you have to ask why I haven't bought any new guns lately, well...there you go.