As FumbleFingers notes in a comment above, a Google Books search turns up many instances in which authors use the verb languished in association with inanimate objects. Here is an Ngram chart for three such phrases—"idea languished" (blue line), "ideas languished" (red line), and "languished unread" (green line)—for the period 1850–2005:
The chart indicates that figurative use of languished didn't catch on until the later decades of the nineteenth century, but it is by no means rare or suspect today. The first matches that a Google Books search finds for each of the three wordings are as follows. From "Philanthropy in War," in Blackwood's Edinburgh Magazine (February 1877):
Thus, nipped in the bud, the idea languished till, in the summer of 1870, the war between France and Germany gave it a new impetus.
From Rene Bazin, "With All Her Heart," in The Living Age (December 18, 1897):
There were sweat-drops visible upon uncovered necks, and now and then the tap of a small boot-heel was heard upon the floor, or the drumming of five fingers upon the table. There were no more happy inspirations. Ideas languished and vanished away in daydreams, and M. Lemarie's death was already forgotten.
And from Louis Vance, The Bronze Bell (1909):
Now Quain's letter to Labertouche went by this quicker route and so anticipated Amber's arrival at the capital of India by about a week; during all of which time it languished unread.
From these examples it should be clear that Merriam-Webster's Eleventh Collegiate Dictionary (2003) is fully justified in including definition 2(b) in its entry for languish:
languish vi (14c) ... 2 ... b : to suffer neglect {the bill languished in the Senate for eight months}
Definition 2(b) has appeared in editions of the Collegiate Dictionary series since the Eighth Collegiate (1973)—so it seems fair to say that, if there ever was a widely enforced rule against using languish for nonliving things, Merriam-Webster gave up on it more than four decades ago.
With regard to direct objects, all of the definitions of languish in the Eleventh Collegiate involve the word's use as an intransitive verb. That would seem to preclude (or at least leave unrecognized by Merriam-Webster) the use of direct objects along the lines of "He languished his life away"; but it certainly doesn't present any barrier to using languish with prepositional phrases, such as "Her paintings languished in a musty warehouse."