Hello again, JoySusan. The hole you dug (congrats on your enthusiasm) held water too well (pun intended). The larger hole you dig the bigger pond you'll make. Sounds like your soil saturated and has too little percolation. A really big hole with poor percolation just delays the inevitable a little while longer, it fills up and retains water, breeds mosquitos, whatever. Disguised in engineering terms, good surge capacity, slow recovery.
In really really bad cases (yours is beginning to sound like one) you can trench under the path where it stands in water, fill with gravel covered with geotextile topped with gravel to walk on. In the graveled trench you need a perforated drain pipe covered with tyvek sleeving (or similar) to collect the water in the trench and start it down the drain pipe. The drain pipe is to lead the water to where it can be safely and conveniently released. This drain pipe must slope continuoulsy down ward (no loop de loop rollor coaster impromptu "traps" else it will retain water in the "trap(s)", breed mosquitos, and smell bad. It must conltinue "downhill" untill it "breaks" the surface or meets a ditch, storm drain, whatever. The "whatever" could be a better location for a dry well.
Several years ago I had a similar problem in an urban setting. My lot sloped to the rear and drained on to the two down slope neighbors. One took out a raised bed on the fence line and replaced it with a retaining wall (cement) reaching 6-12 inches above grade and I put in an "L" shaped outbuilding with slab floor and a course of block as a stem wall to complete the "dam" across the drainage path. My solution was to dig 3 dry wells. One at each end of the "L" shaped shed and the third under the center of the "L". I ran perforated drainage tubing from the two wells at the extremes to the well in the center. All 4 ends were sleeved in tyvek. The center well was covered by the slab floor. The theory was (and it worked in all conditions for well over 10 years) that any runoff from the driveways, house, and yard that headed down slope in the rear of the house would end up falling down a well (insert smiley face here) and run under the slab of the out building to the well at the center where the water would be discharged essentially where it would have gone had there been no new retaining wall or "L" shaped building.
Patrick (No trees were killed or injured in the preperation of this message.)