What happens if you have no oil pressure i.e your oil pump goes out?

You will loose oil pressure and the engine will starve for lubrication. The result will be a lack of oil to the bearings, rings, and valve train. This will cause the engine to overheat, more than likely blow a head gasket, and the bearings, rings, and valve train will wear very quickly. If you continue to drive the car the engine will eventually lock up. The end result will be an engine that is severely damaged and will need a major overhaul to put it right. The good news is that if you shut the engine off as soon as you see no oil pressure then no damage will be done. A new oil pump and it will be fine.