Get rid of the water first.......

I agree with bulldinkie. Otherwise, you're wasting your time and money.

I agree. You need to get rid of the water first. In the meantime you need to get that carpet UP NOW. You could be growing black mold under there. Mold can make you sick big time.

Since youve had water problems I dont think Id ever put carpet back even if you think the water problem is corrected. If it were me Id do some kind of a finish/stain on the concrete itself. That way you could see the water right away and take care of it.

I forgot to ask. Do you have a sump pump. And have you checked your drainage around your foundation and your downspouts.

ditto w/the above posters

Just went through all of that w/our basement - start outside first - especially helpful while downpouring - you may be surprised how the water is flowing off the roof/gutters -
1. landscaping pitched away fr. foundation
2. preferably no large plantings near foundation - they will attract water
3. gutters properly attached, pitched, draining away from home
4. you could try filling the cracks in the foundation to see how that holds up -
5.sump if necessary

Waiting to see if your remedies work keeping moisture/water out before laying new flooring - in the interim get the carpet up/out and treat the floor -