Free tuition at Yale, Stanford/ Harvard?

Don't give up on your dream but apply to some lesser schools. Your application will be good, but the problem is so will 20,000 other applications to those schools. SATs of 1600 (800 math/800 verbal) can be, and routinely are, turned down. If you score a 1300 (a good score on the m/v) your chances will not be very good.