Is Tuesday named for a one-handed god?
1540s, "ineffectual," from un- (1) "not" + available. Meaning "incapable of being used" is recorded from 1855. Unavailing (1660s) has taken up the older sense of the word.
mid-15c., "beneficial," also "valid, effective, capable of producing the desired effect," from avail + -able. Meaning "at one's disposal, capable of being made use of" is recorded from 1827.