Damp spots on basement floor

I pulled up some old foam-backed carpeting in my basement laundry room to replace. The concrete slab is old, and had crumbling concrete patch work, so I set to scraping that all up, seems the more I scrape, the more comes up. AND, all the scraping has revealed 4 small (golf ball sized) patches of damp concrete. Damp to the touch, but not wet, really. A paper towel comes away dry. A few had a small amount of mold under the broken concrete patch. I cleaned up the floor as best I could and have been running a de-humidifier down there for 4 days, with no change.

I was planning on patching up the broken up areas, enough to level it for some more cheap carpeting. It's the laundry room, I'm not concerned with perfection, but now I have two worries. First, is my house going to float away if I don't spend $20, 000 getting my floor ripped out, new drains installed, etc.? Second, if I wait til a dry spell, seal the concrete with something, fill with concrete patch and lay down some carpet tiles, will I go to basement water-proofing hell?

Fact#1: the basement isn't really damp other than the floor patches.

Fact#2:this part of the house is old. Real old. (1880) The floor looks to be block with a thin concrete cap, though, so maybe its been re-done. Fact#3: There is a sump pump, sitting below the floor level, functioning properly, and I can see 2 drain tile openings in the basin. Water looks to be dripping from them, so drainage is working at some level.

The slab in question is smallish, about 100 sq ft, about 2 ft higher than the rest of basement, ( 2 steps up) which is a finished rec room with linoleum finish on floor. The concrete cap is pebbled concrete work, and looks like smooth concrete troweled over to patch in some areas.