Got a 1098-T for 2010 Tax year (when I was considered non-resident for tax purposes) but that amount was paid in 2011 (when I am considered resident). Since Educational credit can only be taken when its actually paid, can I take the American Opp. Credit in 2011 since I am a resident and I paid the 2010 billed tuition in 2011?

No, you cannot claim the credit, because, though paid in 2011, it has been credited for 2010 tuition and reported to the IRS on a 2010 Form 1098-T. If you do claim the credit on your 2011 tax return, the IRS WILL challenge it.

Now, if you contact the college registrar and get them to amend the 2010 Form 1098-T and issue a 2011 Form 1098-T, then you can claim the credit.

I am not sure if the registrar will amend the 2010 1098-t since they only report charges billed to the student and not how much they received.

Also in Turbo Tax, there is a way to enter tuition payments that are not on 1098-t? Wouldn't this qualify? That would exclude me from The American Opportunity Credit but what about the Lifetime Learning Credit which doesn't require you to be in a degree program or have 1098-t to go along with it?

OPTStudent2012:

You are missing the point: The IRS (or, to be more specific, its computer) keys on the Form 1098-T when they review the return. You CAN legally claim the education credits without the Form 1098-T, but the IRS WILL challenge your claim if there is no Form 1098-T in the audit trail to support the claim. In that challenge, they will key your eligibility on this question:

Did the academic period for which you paid qualified education expenses begin in 2011 or the first 3 months of 2012?

Based on your original post, the answer to this question is NO! Once the IRS makes that determination, they will deny the credit.