You might very well have battery voltage at starter relay untill you put a load to the system. There might be enough continety to make the dome light glow but as soon as you load the system it falls on it' face. Have seen this caused by corroded or lose battery clamps and other bad connections. Check voltage at starter relay also with key in 'start' and 'run' position. Voltage might drop a lot when key is turned. Or even easier: Check battery terminals and ground battery - engine -chassis. Hope you get it sorted out.
Lars