A Mooney M20 collided with a gravel pit during the landing roll after a forced landing. The pilot made two attempts to complete the flight. The first attempt was aborted due to the mixture control cable breaking. The pilot safety wired the carburetor to the full rich position. When the pilot took off the second time, he had the fuel tank selector switched to a fuel cell with only thirty-five minutes of fuel. The aircraft is equipped with a single fuel quantity gauge which is switchable to read the quantity in only one of the fuel cells. The fuel quantity gauge was switched to read the fuel quantity of the other fuel cell, which contained about one hour of fuel. After about thirty minutes of flight, the engine lost power. The pilot thought the power loss was related to the discrepancy with the mixture control. He did not attempt to switch tanks. The pilot executed an off-airport landing in rough terrain resulting in substantial damage.