Look at this thread where kelsmom explains the regs on refund disbursements: So when exactly do you get your loans?
It doesn't sound like you have loans and they're obviously not holding funds for 30 days, so you should probably just give them a call and let them know your situation. If your total aid meets all of your EFC, they may release some money or give you a bookstore voucher when school starts so you can buy your books but I'd be surprised if they did so any earlier than that as they can't be sure you'll actually show up in August!
Were any of your scholarships local, where the check was only made out to you? If so, use that money and your grad gift money/summer earnings for your plane ticket. You could also use a credit card (or ask a relative to put it on their charge account for a month til you get your refund). A computer isn't a necessity right away, most colleges have tons of computers for students to use. Some do give computers to low EFC kids who apply for them, so you check to Reed has a program like that.