I cannot say that you have no chance of ever receiving this money. That would obviously be up to the state of NY if they are willing to make an exception in your case. All I can tell you is what the NY law
is, and actually the NY law is the same as the IRS -- and that is that no refunds will be issued to taxpayers for any tax years
filed or amended more than 3 years beyond the original due date of the return.
I do understand your frustration in such a situation, but the state would likely take the position that if you were due a refund of $700 and never received it, that should have alerted you to the fact that possibly your return was never received or processed, and prompted you at that point to make a call or write them a letter to find out where your refund was. If you had done that within the 3 year allowed time period, then you could still easily get any refund that you were due.
If you have actual proof that you submitted your return, such as a certified mail receipt, or if H&R Block was supposed to have filed electronically and you can get a statement from them to that effect, that would certainly help your chances in appealing this. But without actual proof that your return was submitted, it will probably be a little bit of a battle to still get any refund for that tax year.
If I were you, I would go ahead and submit your return for that year along with a letter of explanation and any proof that you have that your return was submitted by the original due date. If they find that what you submit to them is reasonable proof, then they may allow some consideration in your case, but there is no way to say for certain how they may rule on this. I do know that if you had no additional tax liability for that year, then you would not be assessed any penalties or interest.
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Thank you, XXXXX XXXXX of luck in getting this resolved. I hope everything works out in your favor here.