My
B7800 had a problem with the fuel cut off switch. You can hear it 'click' (energizing the switch) when you turn the key to the start position. If that doesn't make contact it won't 'click' and cuts off the fuel to the engine and it'll turn over but not start. This switch cost about $150 and is located by the key switch under the RPM indicator. And yes, everything else had power.
It may not be your problem though as you were able to start it by jumping it. Just make sure you hear that 'click' when you turn the key.