What does this have to do with legal malpractice?
"How can I find out if my check has been cut by the City of New York?"
Not knowing what check you're talking about, I would assume you'd ask a person in the office of whatever city agency is involved.
"The trail settlement was in late January 2008."
You mean trial, right?
"When I call my law firm, all they say is the check has not arrived."
When did you call your lawyer? Assuming it was fairly recently, surely you must have responded by saying something like "when do you expect it to arrive?" and/or "please call the city or its lawyer and ask about it and call me back ASAP."
"Is there anyway to find out if the check has been cut and if the law firm has cashed the check?"
Lawyers and law firms don't cash settlement checks. They deposit them in a client trust account. If your lawyer told you the check hasn't been received, then the firm obviously cannot have deposited the check.