Jump the lives

Could well be your glow plug relay.

Get a jump lead, find the glow plugs, they should be connected by a metal strip/bar, connect the jump lead to it, then to the live on the battery, wait 15 seconds then turn it over.

Give that a go

P.s How exactly have yo uestablished no fuel is getting through?

pps I would put money on it that its your plugs, its got al lthe charactedristics of a plug relay, because when you switched it off, then switched it back on again and it fired up, the engine would have been warm and there would be no need for the glow plugs to do anything.