If Purdue University online is not an Eligible Educational Institution, than none of the 529 withdrawals for any associated expenses are qualified.
Assuming Purdue University online is an Eligible Educational Institution:
Can the school provide you with their allowance for room and board, as determined by the school, that was included in the cost of attendance (for federal financial aid purposes) for online students? If not, than I highly doubt that rent while taking online classes is a qualified expense. The computer would be a qualified expense, provided that it's to be used primarily by the student during any of the years the student is enrolled at an eligible postsecondary school. (This doesn't include expenses for computer software for sports, games, or hobbies unless the software is predominantly educational in nature.)