Last year (for 2009 returns) New York State did not require the EIN of the college. That's why you weren't asked for it. This year (for 2010 returns) New York does require it. You cannot claim the New York tuition credit or deduction without the EIN of the college. The New York State Department of Taxation and Finance might track you down if you claimed the NY credit or deduction without the EIN, but TurboTax won't let you file your return that way, so you don't have to worry about the state tracking you down.
The EIN of the college is not required on your FEDERAL tax return. There isn't even any place to enter it on a federal return. The IRS only looks at your federal return, not your state return, so they don't care whether you entered the EIN or not. They don't even know whether you entered it or not. Since the IRS doesn't care about the EIN, they are not going to track you down if you omit it.