It can be difficult to debug problems like this.
First off, it sounds like you've done all of the usual, intelligent things a person should do.
You've bought enough replacement hardware and tried replacing everything which you suspected was faulty.
What I'd recommend doing is marking each of our Arduino boards, RAMPS boards, A4988 motor drivers boards, and motors, so that there cannot be any confusion or mix-ups.
What you need to do is determine which hardware is good.
Then systematically begin testing them to find out which ones will work and writing down notes on paper.
First find out which of your motors and A4988's are good. If a motor and A4988 work anywhere, then you can mark them both as OK.
You'll want to figure out if either of your RAMPS boards can drive any of your motors on the E0 channel. (I'm assuming that you won't have any problems with the X, Y, and Z channels and you can use them for finding out which 4988's are good.)
Note: often the Marlin or Repetier software running on your Arduino will not allow you to move the extruder motors unless the hotend is hot enough! If you are using the original Marlin from BEL, look in Configuration.h, and you'll see this line:
#define EXTRUDE_MINTEMP 170
That means it shouldn't allow any extrusions unless the hotend is at 170C or above.
You can comment out this line to turn off this behavior.
#define PREVENT_DANGEROUS_EXTRUDE
I'd guess that you might have a damaged A4988 and/or perhaps RAMPS board, but that a crucial part of the problem has been that you didn't know about the above, and it has been playing hob with your testing.
Good luck!