Talented derives from talent, which is not a verb in Modern English.
Has talent ever been used as verb? Are there any words ending in -ed that derive from words once used as verb that is not used nowadays?
Has talent ever been used as verb?
There are no signs of this in any dictionary, etymology dictionary, or online resource I have checked.
Do adjectives ending in “-ed” derive from words that were once used as verbs?
No, not necessarily. Someone is talented because he has talent, not because he was talented by someone or has talented something. As Daniel points out in his answer, there are lots of such constructions: five-fingered, long-legged, lighthearted, etc. These words are not derived from verbs, they are derived from nouns, as Kosmonaut explains in full detail in his answer.
Are there any words ending in -ed that derive from words once used as verb?
Yes. One example is "sacred":
c.1300, from pp. of obsolete verb sacren "to make holy" (early 13c.)
The OED makes a clear distinction between the -ed that forms adjectives and the -ed that forms the past participle (and, naturally, any past participle can be used as an adjective). The adjective-forming -ed (which gives the meaning "possessing, provided with, characterized by") definitely does not have any inherent verb-related qualities, or require that there ever was some verb counterpart at any point in time. You can go straight from noun to adjective, like in your example with talent. Even in cases where there is a verb form, e.g. feathered, there is nothing about "feathered bird" that suggests that this feathered came from the verb (i.e. nobody ever feathered the bird). Compare that to "fallen soldier", where adjective fallen clearly did come from the past participle fallen (i.e. the soldier did fall).
The reason the adjective suffix looks like the past suffix is because they originally came from the same etymological root. The OED says (modified to have less abbreviations):
-ed is appended to nouns in order to form adjs. connoting the possession or the presence of the attribute or thing expressed by the noun. The function of the suffix is thus identical with that of the Latin participle suffix -tus as used in caudtus (tailed), aurtus (eared), etc.; and it is possible that the Teutonic -ôjo- may originally have been from -ôo- (see past ppl. -ed), the suffix of past participles of verbs in -ôjan formed upon nouns.
The OED also says that there are many cases where it is impossible to tell 100% for certain which -ed adjectives were originally from past participles of verbs that later disappeared, and which were just formed straight from nouns, but surely there are some of the former.