I want to set the starting point of my graph (both in the x- and y-axis) to be zero. I have used the xlim() and ylim() functions to no avail. I have at
Your axes do start at 0, and xlim and ylim are what you need to change that.
What I think you are referring to is the spacing between the axes and the plot.
There are two extra parameters that allow you to change that, xaxs and yaxs.
plot (x, y, xlim=c(0,10), ylim=c(0,10),
xaxs="i", yaxs="i")
This should do the trick
See the par help for more info.