I would use sullied because sullied means ruined and in this soliloquy Hamlet is talking about how he wishes his body could simply melt and why God has made suicide against the law. If suicide was not against law or religion then Hamlet would take his life immediately to get away from his sea of troubles that is troubling him.
There are three received texts of Hamlet. The 1st Quarto (Q1) from 1603 uses "sallied". The 2nd Quarto (Q2) from 1604 also uses "sallied". The Folio (F) from 1623 has "solid". Harold Jenkins in his Arden Hamlet 2nd ed. uses "sullied", relying on J. Dover Wilson's The Manuscript of Shakespeare's 'Hamlet' and the Problems of its Transmission. Also see Fredson Bowers' chapter, "Hamlet's 'sullied' or 'sold' flesh: a bibliographic case-history (1956)", pp123-127 in The Cambridge Shakespeare Library Volume I Shakespeare's Times, Text and Stages. Essentially, Wilson claims that "sallied" is a printer's error, mistaking a 'u' (of sullied) for an 'a' making the word "sallied". While I agree that "sallied" is the least favored, I think it is an even split between the other two. "Sullied" conveys more the tone of the soliloquy. "Solid" is more fitting to the context of Hamlet's initial line of thought. Personally, I would go with "solid" just because I prefer the Folio emended with the Q2 rather than the other way around. It is difficult for me to separate the two. Knowing the background on this point I tend to hear both words while reading the play or hearing it in performance.