The Collaborative International Dictionary of English v.0.48:

Heartsick \Heart"sick`\ (h[aum]rt"s[i^]k`), a. [AS.
   heortise['o]c.]
   Sick at heart; extremely depressed in spirits; very
   despondent.
   [1913 Webster]

WordNet (r) 3.0 (2006):

heartsick
    adj 1: full of sorrow [syn: brokenhearted, heartbroken,
           heartsick]
    2: without or almost without hope; "despondent about his
       failure"; "too heartsick to fight back" [syn: despondent,
       heartsick]

Moby Thesaurus II by Grady Ward, 1.0:

29 Moby Thesaurus words for "heartsick":
   blue, cast down, comfortless, crushed, cut up, deep-troubled,
   dejected, depressed, desolate, desole, disconsolate, dispirited,
   down, downhearted, forlorn, heart-stricken, heart-struck,
   heartsore, inconsolable, miserable, sick, sick at heart, soul-sick,
   stricken, suicidal, unconsolable, woebegone, woeful, wretched