** I have turned off the Main Water Supply, and have tried to drain the Cold Water Feed to the Pipe with the "Pin Hole Leak"....The Water is still Dripping!! **
Hopefully it doesn't mean your main shutoff isn't closing fully.
** What can be done about this? **
You can try opening a couple of taps, one above the section you need to work on AND one below, to allow any remaining water to drain out the tap at the lowest connection by gravity. Pipes won't fully drain if there isn't a way for air to get in and replace the water that is there.
** I need to replace this section1 **
If you're replacing that part of the pipe, just cut the section out with pipe cutters. A pipe cutter doesn't need the water to be removed (although there will likely be some spillage which you should prepare for with a bucket, etc.)