After a few days like that, the body will begin to sense starvation. After more than 2 weeks like that, a real effect of starvation will set in and health problems may start to occur.
About 1 to 2 days, but in that period of time you will mainly just lose water weight and could continue to be just water weight for up to 4 days. By 7 days your body will be fully in the starvation...
How long one can live without any solid substance is quite long. A couple of IRA-prisoners lived soly on water and salt for about 40 days before starting to go under. But if you remove everything.....