There are a couple options that will require little equity depending on the number of units in your home (whether it's a single family or a multi-family residence).
I can go over this in more detail if you want to email me, I'll keep it short so the Realtors/Inspectors/Attorney's can address the "who did what".
I'm not sure how the disclosure laws work in your state. Since you didn't provide a lot of information, I would ask the following:
1. Did you use a real estate agent, and did the contract you used include a contingency period to get a home inspection by a qualifed professional? Why wasn't this problem uncovered prior to closing?
2. Did you get the home inspected prior to closing? If not, why?
3. Was the home sold AS-IS? Or, did you get the home at a price that reflected the price of any needed repairs?
4. Did you view the home prior to buying it?
In my opinion, you probably would not have much recourse at this point. You would most likely have to prove A. that the seller was aware of this defect, and "hid" it purposely in an attempt to deceive/defraud, and B. explain the due dilligence performed on your part as the buyer - and how/why this issue wasn't, or couldn't be, uncovered by you prior to closing. Again, since I'm not familar with NY disclosures and the laws surrounding it, nor am I a lawyer, I can't comment on if you would in fact have any recourse. I would contact a real estate attorney, and/or a real estate agent in your state to get a more specific answer.
No one wants to be the bearer of bad news, which may be why you don't have a response yet. I am a licensed realtor in North Carolina, so can only represent what would legally apply in my state. What you need to find out is if NY is a caveat emptor state - Which means "buyer beware." Which is appears it is in this article:
Typically, after the real estate transaction has been closed - there is limited legal recourse against the seller, also the seller has no legal requirement to disclose everything they know about their property. However, your realtor, with a signed buyer agency agreement, has fiduciary responsibility to discover material fact and disclose any material fact that may alter your decision to purchase the property. If there is reason to believe that the rot problem was intentionally hidden from you or misrepresented, AND you and your realtor made every reasonable effort to discover and repair any issues before closing, then you may have a case.
Also, I would reference the home inspection, depending on where the rot is and the severity of it, it should have been noted on the home inspection - which also should have been addressed before closing. If the rot is as severe as you say it is, and depending on where it is, you may have recourse against the inspector. Ultimately though, in North Carolina and caveat emptor states in general, unless reasonable and "should have known" material facts were intentionally hidden from or misrepresented to you in the buying process, I'm afraid you may have limited recourse against the seller.
Again, can only speak of the laws in North Carolina, but according to the above posted article, New York seems to have a similar structure. I would recommend reaching out to your realtor, if you hired them, as well as an attorney that specializes in the real estate industry for a second opinion.
Hope this helps,
Disclaimer: I'm not a lawyer, so this isn't legal advice. Further, I'm not licensed in New York, so I can't specifically address your contract. However . . .
Was the house sold as-is? If so, that doesn't totally exonerate the seller, but it can put more of a burden on you.
Or--and I don't know how New York works--is the seller required to disclose known defects? If so, and (here's the catch) you can show that the owner knew about the problem, you may have recourse against the owner. On the other hand, some states also allow a seller to "disclaim"--meaning the owner essentially is saying: "I don't know."
Related to the previous point, was the real estate agent who listed the property aware of the rot? If so, it should have been disclosed. (The agent could have been aware either through statements from the seller, or from a previous home inspection that she was privvy to.)
One other question: Did YOU have a home inspection done? If so, and if the rot should have been apparent to the inspector (that is, visible, not hidden), then you may have recourse against the home inspector.
Check with your Realtor for more information.
Hope that helps.