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]

Moby Thesaurus II by Grady Ward, 1.0:

56 Moby Thesaurus words for "busted":
   aggravated, bankrupt, beat, broke, broken, burned, burst, checked,
   chipped, cracked, crazed, cut, damaged, destitute, deteriorated,
   embittered, exacerbated, failed, flat, flat broke, harmed, hurt,
   impaired, imperfect, in bits, in pieces, in receivership,
   in shards, injured, insolvent, irritated, lacerated, mangled,
   mutilated, on the rocks, oofless, rent, ruined, ruptured, scalded,
   scorched, shattered, slashed, slit, smashed, split, sprung,
   stone-broke, stony, strapped, the worse for, torn, weakened, worse,
   worse off, worsened