What is the cheapest way to repair a crumbling basement floor?

If there is moisture/water coming up through the floor there is nothing that can be done to prevent it. That will need to be solved first. You can fill the missing pieces with a latex modified concrete mix. For the crumbling and dust you would need to clean the surface well. Then you can use a concrete resurfacing compound .

https://www.quikrete.com/athome/video-resurfacing-concrete-slabs.asp

Concrete basement floors can only be repaired using concrete according to these articles Sherry. Sounds like a DIY project that will take time and patience.

https://www.doityourself.com/stry/how-to-repair-concrete-basement-floors

https://www.ehow.com/how_12166128_fix-crumbling-cement-floor.html

Thank you

I have a crappy basement floor, always had water come up. Since getting the baseent waterproofed and a sump pump in, my 100 yr old fieldstone basement is very dry, not a hint of mustiness.

I am thinking yours should be too? Is this a continuing problem? I would contact whomever did the waterproofing. If you have water coming in, it isn't waterproof.

You should not paint a floor that is continually damp as this will cause the paint to peel and only make a mess for you to clean up. You need to stop the water from entering your home so take a look at the outside foundation and put in some weeping tile. A lot of work, but your problem will go away if you put the tile in and run the water away from your home. If that is too much expensive, you can put in a piped trench all around the perimeter of your floor and run the water into a drain. This would help to keep the main part of your floor dry.

Thank you