To further comment on the already good advice: moving your high limit screw will not KEEP the front derrailer in the far right position...it only lets the cable pull it that far.

Cable tension is what keeps it in place, if it doesn't stay put, that's the only reason. In fact, once the cable is about the right length (it might not be, if it is really stretched, or installed badly)...you should be able actually see the derrailer move to the right as you adjust the barrel adjuster.