Hmmm, I wonder if the previous homeowner has the answer. And is the basement recently finished, and by whom?

Find water source by process of elimination and it's not that easy. It could be the snow pushed up against the house, causing pressure of rain & snowmelt to find a way in. It could be clogged gutters, followed by the downpour, which may have caused water to go over the backside of the gutter and behind the wall and down, etc.

I might open up the inside walls in a few places and take a look at the moisture stains. If they're up at any joists, the problem is above. Or maybe there are some foundation cracks that need to be delt with (sealed by injection, for example).

Might ask the neighbor if they know anything, too. Good luck.

Don't hesitate to get the dehumidifier and ventilation fans going down there. Needs to be done ASAP.

thank you Homebound,

The basement was finished a number of years ago, by I believe the original owner, but I could be mistaken about that. I'm not sure when the most recent carpeting was put in either.
My husband did speak with the previous owner, before they moved out. He mentioned that there had been a water problem at one point, caused by a downspout, but the problem area had been repaired.
We had a house inspection done before closing on the house, and he saw no evidence of an active water problem.
We viewed the house at this time last year as a matter of fact, and one of the things we noticed was that the basement did NOT have a "basement smell" to it at all.
One thing we've noticed is that there is no visible floor drain anywhere in the basement, that we have seen.
I'm wondering what the odds are that it is under the carpet in the rec room??
I've been running the dehumidifier non stop since discovering the wet floors.
I'm just so overwhelmed by this whole process of trying to find the source, and then figuring out how to prevent it from happening again, once all this ice and snow starts to melt in the next month or so.
:o(