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Perhaps it is related to Middle Low German keie "lance, spear" on notion of "tool to cleave with," from Proto-Germanic *ki- "to cleave, split" (cognates: German Keil "wedge," Gothic us-kijans "come forth," said of seed sprouts, keinan "to germinate"). But Liberman writes, "The original meaning of *kaig-jo- was presumably '*pin with a twisted end.' Words with the root *kai- followed by a consonant meaning 'crooked, bent; twisted' are common only in the North Germanic languages." Compare also Sanskrit kuncika- "key," from kunc- "make crooked."
Modern pronunciation is a northern variant predominating from c. 1700; earlier and in Middle English it often was pronounced "kay." Meaning "that which holds together other parts" is from 1520s. Meaning "explanation of a solution" (to a set problem, code, etc.) is from c.1600.
The musical sense originally was "tone, note" (mid-15c.). In music theory, the sense developed 17c. to "sum of the melodic and harmonic relationships in the tones of a scale," also "melodic and harmonic relationships centering on a given tone." Probably this is based on a translation of Latin clavis "key," used by Guido for "lowest tone of a scale," or French clef (see clef; also see keynote). Sense of "mechanism on a musical instrument operated by the player's fingers" is from c. 1500, probably also suggested by uses of clavis. OED says this use "appears to be confined to Eng[lish]." First of organs and pianos, by 1765 of wind instruments; transferred to telegraphy by 1837 and later to typewriters (1876).
"piece of timber sawn flat and thin, longer than it is wide, wider than it is thick, narrower than a plank;" Old English bord "a plank, flat surface," from Proto-Germanic *burdam (source also of Old Norse borð "plank," Dutch bord "board," Gothic fotu-baurd "foot-stool," German Brett "plank"), perhaps from a PIE verb meaning "to cut." See also board (n.2), with which this is so confused as practically to form one word (if indeed they were not the same word all along).
In late Old English or early Middle English the sense was extended to include "table;" hence the transferred meaning "food" (early 14c.), as "that which is served upon a table," especially "daily meals provided at a place of lodging" (late 14c.). Compare boarder, boarding, and Old Norse borð, which also had a secondary sense of "table" and an extended sense "maintenance at table." Hence also above board "honest, open" (1610s; compare modern under the table "dishonest"). A further extension is to "table where council is held" (1570s), then transferred to "leadership council, persons having the management of some public or private concern" (1610s), as in board of directors (1712).
"Bow to the board," said Bumble. Oliver brushed away two or three tears that were lingering in his eyes; and seeing no board but the table, fortunately bowed to that.
Meaning "table upon which public notices are written" is from mid-14c. Meaning "table upon which a game is played" is from late 14c. Meaning "thick, stiff paper" is from 1530s. Boards "stage of a theater" is from 1768.