Does buying in installments from a commercial store through an interest-based bank—with the buyer's knowledge of this after the procedures have been completed and his fear of not being able to back out—count as one of the major sins of usury?

The method used by the shop to sell the computer is considered an interest-based loan (riba), and you must withdraw if possible. However, if the matter is beyond your control and you were not negligent in inquiring, then there is no sin upon you, and the sin falls upon those managing the shop. Rectifying your situation with the bank by expediting the payment without waiving the interest is not necessary and serves no purpose other than accumulating interest for the bank and accelerating the principal.