The Collaborative International Dictionary of English v.0.48:

damaged \damaged\ (d[a^]m"[asl]jd), adj.
   1. changed so as to reduce value, function, or other
      desirable trait; -- usually not used of persons. Opposite
      of undamaged. [Narrower terms: battered, beat-up,
      beaten-up, bedraggled, broken-down, dilapidated,
      ramshackle, tumble-down, unsound; bent, crumpled,
      dented; blasted, rent, ripped, torn; broken-backed;
      burned-out(prenominal), burned out(predicate),
      burnt-out(prenominal), burnt out(predicate); burst,
      ruptured; corroded; cracked, crackled, crazed;
      defaced, marred; hurt, weakened;
      knocked-out(prenominal), knocked out; mangled,
      mutilated; peeling; scraped, scratched;
      storm-beaten] Also See blemished, broken, damaged,
      destroyed, impaired, injured, unsound.
      [WordNet 1.5]

   2. Rendered imperfect by impairing the integrity of some
      part, or by breaking. Opposite of unbroken. [Narrower
      terms: busted; chipped; cracked; crumbled,
      fragmented; crushed, ground; dissolved; fractured;
      shattered, smashed, splintered; split; unkept,
      violated] Also See: damaged, imperfect, injured,
      unsound.

   Syn: broken.
        [WordNet 1.5]

   3. being unjustly brought into disrepute; as, her damaged
      reputation.

   Syn: discredited.
        [WordNet 1.5]

   4. made to appear imperfect; -- especially of reputation; as,
      the senator's seriously damaged reputation.

   Syn: besmirched, flyblown, spotted, stained, sullied,
        tainted, tarnished.
        [WordNet 1.5]

The Collaborative International Dictionary of English v.0.48:

busted \busted\ adj.
   1. Inoperable due to damage; broken; -- of a machine; as, the
      coke machine is busted. [informal]
      [WordNet 1.5]

   2. Arrested for committing a crime; -- of a person; as, the
      rock star was busted for coke possession.. [informal]
      [PJC]

   3. [predicate] same as demoted; -- said especially of
      military rank, and often folowed by to; as, he was busted
      to corporal for being AWOL.
      [PJC]

   4. [predicate] same as exhausted; -- of people.
      [PJC]

WordNet (r) 3.0 (2006):

busted
    adj 1: out of working order (`busted' is an informal substitute
           for `broken'); "a broken washing machine"; "the coke
           machine is broken"; "the coke machine is busted" [syn:
           broken, busted]