If it's ground water, the issue isn't water vapor, but rather just plain water. Is the water table close or higher than your basement slab? If so, not a whole lot you can do to completely stop moisture issues, as that basement was just built in a bad spot.
That said, the main solution would be a sump pump and drainage tile system. Any water coming up through the earth dumps into the drainage tile, into the pump well, and gets pumped out. Again, though, if the water table is already higher than the basement slab, that'll be a never ending battle as well.
That said, perhaps the issue isn't as much about ground water as you think. Does it get humid in your region? If so, then 'damp' basements are par for the course. Basement walls are usually always going to be cooler than the air, and, a such, will be were condensation forms in a humid environment.
To prevent that, you need to a) dehumidify and/or b) insulate the walls.
A dehumidifier constantly running tends to be a normal part of any basement in a humid zone, so that's a good start. Insulating with walls with XPS or EPS foam will help too, it'll keep the moist air further away from the cold wall.
I can't say if an air exchanger would help or not. If it's including an A/C system, it could help (as the A/C is a dehumidifier) but otherwise I have a hunch you'd just be pumping more humid air into the space.
Products like drylock don't do a whole lot. They're not strong enough to prevent hydrostatic water pressure (high water table) and do nothing to prevent condensation. They're a bit of a gimmick.
The fact that the water is seen in the pit only after a rain is a good thing, meaning your water table is not the problem, because that would mean a sump pump for sure. I think you are just seeing this because the valve is only 2' from the wall. Normally, it was dissipating. You had a good wall/slab system that wasn't leaking until a hole got poked in the slab for the repair
Some grading of the soil alongside this wall for better runoff might be in order. Any drainspouts nearby?
Some ad-hoc pump automation in the pit would give you some peace of mind until you can get outside for some landscaping.
Self contained sump pump
To verify gutters-to-storm drain are intact and not leaking down at the slab level,
Put a bottle of easter egg dye into the storm drain connection. If you see the color in the pit, I would disconnect the downspouts and direct them into the yard.
A pain for mowing, but the flip up ones work well. In our area, downspouts were connected into the floor drains and thence to the sewer. In the 1990s, we had to cap the connection with concrete or face a fine.
Best Answer
EDIT TO ANSWER YOUR SPECIFIC QUESTION: Yes, whatever you can do to direct water away from the foundation wall will work. My neighbor, literally, just stopped by to borrow a circular saw so he can cut some plywood into 2'x4' sheets to lay against his house to direct water away.
Mass real estate owner here with same problem in 3 different properties. All rubble basements get water, especially in Mass in October.
On the outside:
When it gets dryer or in in the spring, dig out about two feet down (deeper if you can) and a foot out from the foundation and fill it with cement to 3 to 6 inches above the surrounding dirt, sloped away from the house It'll take 5 bags of cement for each horizontal foot (or thereabouts), so you could end up hand mixing 30 to 50 bags depending on the horiztonal run. As you poor the cement, feel free to lay in some chicken wire or other metal mesh or screen to strengthen.
On the inside:
Buy a dehumidifier with a humidistat and leave it plugged in to help speed drying. (another edit: get it to drain into a basement drain or sink....otherwise it'll fill with water and shut off...pain in the ass to empty...build a shelf high up in the basement to put the dehumidifier on..above the sink if there is one...)
Install a sump pump. Of course, if you go to Home Depot today, when it's pissing rain, they'll all be sold out. Dig a hole in the lowest point of your basement and put in a sump pump. I won't explain it all here, but any homeowner can do it. Google "install sump pump"
http://www.mountprospect.org/Modules/ShowDocument.aspx?documentid=2886
In theory you can drylock from the inside, but I've had no luck with it. You can also spray foam insulate from the inside - saw that on This Old House, but I think it would make a hellamess.