Wood between slab allowing ground water seepage
Where I live, we have ground water issues year around. This is obviously subterranean water, (i.e.:  you say, not roof, no water leak, etc.  I also assume no window leaks, because you say it's in the recessed room...only.)

Your first paragraph is powerful. Because the ground seems to "go down towards the foundation," I suspect there is a subterranean water problem caused by: 1) shallow water table, and/or 2) subterranean water pressure. 

1) Shallow water table: if the "area" around your home is generally flat, rain will greatly affect the water table. You say, "have not had a heavy rain in over a week, maybe two," makes me think you get "heavy rain" from time to time. If so, that water will make the water table rise and put water "pressure" on the bottom of your slab...especially the lowest slab. 

Where I live, we'll install French drains under slabs to make sure the water from the water table is diverted away.  Btw, those roof drains that you connected, did you extend them to a stormwater system, or just run them to a ditch where they can seep back down in the ground?

2) Subterranean water pressure: if you live near a hill, the water table will generally follow the  slope of the hill. If your homesite was cleared off along that slope, (or especially if you live near the base of a hill,) the pressure from the water table above your home will push on the water table at the base of the hill and cause the water table to rise. This is called Subterranean Water Pressure AND it will put water pressure on the bottom of your slab. 

The only way to relieve this pressure is to install French drains around your house. The size and depth depends on your site, (slope,etc.) and soil conditions. Remember, you are trying to lower the water table. So, after you gather the water in the French drain, make sure it is discharged off site. Don't let it seep back in the ground. This may take a pump.