Should I disclose academic misconduct on a grad application? I am applying to a master's programs right now and am in a bind.

My professor accused me of academic misconduct in one of my undergraduate classes. After I submitted my assignment I had asked a question on an online forum about an assignment and posted a short excerpt of my work. I was asking a question out of intellectual curiosity to better my work for the future.

This had not been an issue with other professors in our department. This professor was strongly against posting anything online, so he found my post online and stated that I violated his rule of knowingly or unknowingly making my solutions available to other students. I had no intent to cheat, and I didn't feel anything I posted was a solution since they were short snippets of code. I felt this charge was a stretch, but the school sided with the professor and he will fail me for the class.

My school says the records of this academic misconduct process are sealed, and there will be no notation on my transcript, just the failed grade.

Graduate school applications ask if one has been involved in any type of academic hearings and to explain the circumstances. The application also asks me to explain any failed grades.  I fear if I disclose all this information it will hurt my application. As far as I know the graduate school will not be able to find out there was any misconduct, unless they contact student affairs and I permit them to see those records. The graduate school just requires the official academic transcript. I'm wondering if graduate schools also check other academic records.

Any guidance on what I should do?
I don't see what the "bind" is.  You are being unambiguously asked to disclose something, so....you should disclose it.  If you just mean "Oh no, behaving ethically may not be in line with my purely selfish interests": right, this is how ethics usually work.  You shouldn't lie, cheat, steal, injure, rape, murder...even when you think you won't get caught.  That's what "shouldn't" means.  

That they also ask you to explain your failed grades is a good break for you: you should explain carefully what happened.  If at all possible you should enlist a sympathetic faculty member to write something corroborating your story in their recommendation letter.  If you are fully believable then you have a shot that those who are evaluating your application will actually believe you.  They may well think that the professor went overboard and end up weighting the failing grade less strongly than a failing grade that was awarded because you (say) failed the final exam.  In fact, if there is something objective you can do to show that you have mastered the material of that course -- e.g. doing a reading course with another faculty member -- then I strongly encourage you to do so.  

[I'm kind of annoyed to add this but...your academic dishonesty is not in any way protected information.  For all you know, your letter writers could bring it up independently of what you tell them.  Or -- much worse -- when you are N years into your graduate program, your old professor could meet someone in your new program and happen to discuss you.  If it transpires that you were dishonest on your application, that could be grounds for dismissing you from the program.  You sure don't want that to happen.  Sigh -- be good; big brother might actually be watching.]