Kudos to our host provider Hosting Matters who, after breaking out "a bigger hammer" (no, really!), figured out it was actually an overloaded log file causing the problem. In other words, the blog software sitting in its wheel chair on its porch swinging its cane did not suddenly have a heart attack; it was the damned fool kids on the lawn causing the problem.
I'll probably still upgrade it. Maybe.
Pictures of all sorts of things to follow...
And if you're looking for a hosting company for anything, head out to Hosting Matters. They rock!