Sharon, if I'm understanding you correctly, part of the problem is likely due to the previous owner. You do not ever want to caulk the underside of the boards on lap siding. If they did a thorough job of caulking, it probably stopped water at first, but it would also totally close off needed air flow behind the siding, causing the siding to shrink & swell more than normal.
Now, with the lower edges caulked, and leaks coming from points unknown, water which would normally have the chance to escape back to the surface of the siding has no place to go but inside the wall until it reaches the bottom of the siding.
I'd agree that this wall, even by itself, needs attention. I'd definitely look into removing this siding, not going over it; the outer shell needs to be able to breathe or the problems will only be buried below another layer.