Well, one possible solution to stop water getting in down the road could be drylock paint on the interior. however it has its downsides that can, in the long run, be worse than the water getting it. The best, and by far most expensive, is digging up around the foundation and putting on a sealer. Could also install a sump pump
Or move 27,000 miles north where it gets to cold and we have to much ice for water to get in during the winter
Sump pump requires electricity... so they'd need a generator, too.
From the descriptions at hand, I suspect that the proper fix is to seal the foundation, add a french drain or similar approach. Might be able to address some of it with simple grading fixes, too.
Bottom line, not cheap -- but get the right input from experts who are able to examine it. Foundations are important... whether in martial arts or houses.
I'm not caught up yet on this thread, so the Hobbit might have answered this already.
Painting isn't an option - simply too much water coming in (up to 10-20 gallons a day). There's standing water within minutes. The immediate answer is trenching and sump well/pump in the slab on that part of the foundation. The suspicion is that there's a small spring back there - it is highly unlikely the current flow is still from the rains nearly 2 weeks ago. The area we are in is full of small springs, and they think the added water pressure just overcame the sealing that was done (something like Drylok). Eventually, I'll probably want to try do do something on that side of the house on the outside, but we'd be talking about excavating many feet deep (the seepage is about 11 feet below grade), so a major expenditure that's not possible right now.
So, hoping the sump pump can handle things, as that's only $1,500.