The student pilot reported that, during the preflight, he and the non-CFI pilot rated passenger inspected the fuel sumps on each wing and the engine, "pulling [a] sample on each". He added that, during departure from the airstrip, after they became airborne for approximately 9 seconds, the engine "failed dropping rpm to an idle". He added that the propeller was still rotating, but the airplane's engine was not producing power. Subsequently, the airplane landed in a cotton field, the nose landing gear sheared off, and the airplane came to rest nosed over. The airplane sustained substantial damage to the tail and fuselage. The student pilot reported that the airplane had gone through a pre-purchase inspection the previous week and the airplane had accrued little time since the annual, which was 7 months prior to the accident flight. He added that it seemed like the airplane was starved for fuel. The Federal Aviation Administration inspector reported finding substantial water in the gascolator.