A circuit needs to be complete for something to work. If you've checked the battery post connections, then check the other ends of the cables. With your multimeter, check across each connection: battery post to clamp (positive and negative), battery ground cable to frame, ground strap to engine bellhousing, and ground strap to engine block. If you get more than 1 ohm across any of them, then clean them and reconnect. Connections can be good enough to operate small loads (lights, etc.) but fail to provide enough power for larger loads such as the starter.
