Drainage problem

I'm dealing with a knotty drainage problem, which has many parts and isn't quite right for any single forum here but is related to many. So I figured I would start here.

A year ago, I bought an off-grid house in the humid northeast. The house is built on a hillside, which slopes up very steeply behind the house and slopes down more moderately in front of it. No drainage work was done, and perhaps as a result the back yard (between the house and the hill) is a swamp. I would like to drain it.

To figure out the best way of draining it, I would like to understand where the water is coming from. Is it all surface runoff from the hillside and the roof, or is the water table here high for other reasons? What leads me to be suspicious is that there is a disused well on a three-foot-tall hummock in the back yard, and as of January the water level in the well was...three feet down, i.e. level with the surface of the ground elsewhere in the yard.

Now, my question: Is there a good way for a layman to distinguish between a water table that is high because of surface runoff, and one that is high because of water welling up out of the ground?

Many thanks.

Andrew, does the house have a basement or crawlspace? Any water in there?

Does the front yard seem to have any water seeping out anywhere? Is it dry?

What is your soil like? Sand, clay, mulch, forest, etc?

What is at the top of the hill? forest, other houses, water ?

Can you dig a swale at the base of the backyard hill and divert the water that may be flowing down the hill, around the sides of the house and to the front yard?

Many thanks for the good questions, Miles.

Crawlspace, built on slab on grade. No standing water, but high humidity (75%). Probably coming up through the slab, which doesn't have a capillary break.

Front yard is moist, but no standing or running water.

The slab was poured on top of a gravel pad. But per the soil map, the native soil is a shallow (16-31" to bedrock) silt loam derived from glacial till. This extends up the hillside, too, where there are stretches of exposed ledge. Supposed to drain well, but not in my back yard!

There's 100 feet of hill above the house, all recently logged woods.

There is already a ditch around the back of the yard, dug before and separately from the house. (There was a farm here in the 19th century.) Soil from the ditch was used to create a berm on the downhill side. But water appears to be passing through the berm and/or coming up out of the ground in the yard itself.

Clearly the ditch needs to be fixed: Clean it out, check grade, waterproof. (How does one waterproof a ditch??) But if I'm dealing with more than surface runoff here, fixing the ditch won't necessarily fix the problem.

Any further thoughts?

Sounds soggy

What height drop do you have down hill of the house? I'm wondering if your drainage of the damp patch could become a resource further down hill. Perhaps case the spring head and run the outflow around the house to a pond or tank? That near the house, and that shallow, I'd be a bit concerned about potential contamination for using it as drinking water but you could get it tested.

Good thoughts, Michael. There's plenty of space downhill to do whatever I want. The old well, at least, is known to have bacteria in it, so I assume that the groundwater around it does too.

The question is: Is there a spring head? How do I go about figuring that out, and finding it if there is one? How do I distinguish a spring-fed backyard swamp from a runoff-fed one?