Resistentialism is a jocular theory in which inanimate objects display hostile desires towards human beings. —Wikipedia
Unfortunately, as far as I can tell Hamilton only used "the total depravity of inanimate things" as an epigram (I can only find it as a Wikiquote, no mention of what book) after reading the essay of the same name by Katherine Kent Child Walker in the September 1864 issue of the Atlantic Monthly. Walker writes:
I believe in the total depravity of inanimate things... the elusiveness of soap, the knottiness of strings, the transitory nature of buttons, the inclination of suspenders to twist and of hooks to forsake their lawful eyes, and cleave only unto the hairs of their hapless owner's head.L. M. Montgomery uses the phrase again fifty years later in Anne of the Island from 1915.
"It is when my umbrella turns inside out that I am convinced of the total depravity of inanimate things," she said gaily.