The lights on 99% of mowers are ac powered and do not get their juice from the battery, so forget the lights having anything to do with the other stuff not working.
Like the last thread said, check the safety switches. There is one on the brake/clutch pedal, the mower should be in neutral and usually there is a switch for that lever, there is a seat switch so check that one, and there is a blade on-off switch so check it.
There should be 12 volts coming from the ignition switch to the starter solenoid when the key is turned to crank the engine. If you have no volts there, its either a safety switch not made or a bad ignition switch. On an outside chance, and this did happen to me, the battery ground wire where it bolts to the frame had corroded and was insulating the contact, and the bolt was tight. Bottom line, check all connections and safetys.