Can I claim the money I used to help my college student with room and board and other expenses?

Room and board plus living expenses are not qualified education expenses so are not entered on a tax return.

The only qualified education expenses paid out-of-pocket that have an effect on your taxes, are tuition, books, and lab fees. That's it, with no exceptions. Room and board are "NOT" a qualified education expense for scholarships, grants and out of pocket money. Room and board "is" an unqualified but allowed expense if paid with 529 funds distributed in the same year the expense was paid. The room and board paid with 529 funds must also be "in direct support" of the education.

If the student lived at home or with friends and did not pay rent or buy food with that money, then it's not tax free.

If the student used the money to pay rent and buy food for a semester (including the summer semester) that they were not enrolled as a full time student, then the distributions used to pay for those months they were not enrolled "is" taxable income.

Simple answer: No.

But, it depends on the details.

You specifically ask about room & board and "other expenses".  You don't mention how his/her tuition, fees and books  ("Qualified educational expenses" - QEE) were paid for.

If QEE were paid by loans and/or scholarships, you may still be able to claim a tuition deduction or credit, if he qualifies as your dependent. If he is your dependent, you can claim the tuition credit even if he paid the QEE or had it paid by loans.

Furthermore there is even a loop hole available if scholarships paid QEE. The student reports all his scholarship, up to the amount needed to claim the American opportunity credit, as income on his return. That way, the parents  (or himself, if he is not a dependent) can claim the tuition credit on their return. They can do this because that much tuition was no longer paid by "tax free" scholarship.  You cannot do this if the school’s billing statement specifically shows the scholarships being applied to tuition or if the conditions of the grant are that it be used to pay for qualified expenses.

Using an example: Student has $10,000 in box 5 of the 1098-T and $8000 in box 1. At first glance he/she has $2000 of taxable income and nobody can claim the American opportunity credit. But if she reports $6000 as income on her return, the parents can claim $4000 of qualified expenses on their return.