Have a good look at the gutter in case it is dripping.
Is the front patch paved? It is quite likely to be above the original ground level, and also might be sloping towards the house so that water runs to the wall.
The plinth is very likely bridging the DPC. It may have been added to hide (it does not cure) damp, and will have made it worse.
There is a good chance you can cure it by hacking off the old plinth and digging a trench against the house wall. This will enable you to see any water getting in, find the DPC, and will expose the lower brickwork, which can start to dry out when exposed to air. Damp does not easily rise more than two or three courses in good clean brickwork exposed on both sides, with no render, plaster, rubble or choked cavity against it. Also put in some more airbricks.
If, by taking up a board, you can see the rubbish filled cavity against the dwarf wall, it is possible to clear it. Some people use a fabricated tool like a long spoon. But if you can get a builders canister vac, with a steel (not plastic) tube, it will suck up loose sand and mortar. You can loosen it by poking with a piece of iron, or there might be a small gardeners tool to rake it. A large drill would also loosen it, though I have not done that.
When slate is used as a DPC, it is (almost) invariably run continuously, at the same height, all round the house. So once you have found it, you will know where it is. Slate lasts at least 300 million years and does not degrade. If the wall cracks, the slate will crack too, this is not a common problem. Much more common is a bridged DPC, choked airbricks, and blocked cavities.
It sounds like you have found some scraps of slate used as packing under joists where the dwarf wall was not flat and level.
I can't make out your later pictures. Move back to get a wider view, and include something to show scale.
It's also possible that water may be coming from a leaking water pipe. I haven't come across high groundwater in my area, it's generally drains, rain, or plumbing. I do however have a neigbour whose cellar floods in high tides.