I have a similar problems with two boards.
I have a total of 3 Mega 2560 R3 boards. The first one works as it is supposed to.
The second board does not show up when I connect it to a computer. I have tried it one three different PCs and usb cablescables. I used Win 7 64, 32. The computer does not even show the "New Device Found" notification.
The third board shows up good, the COM port is assigned but I am unable to program it. When ever I try to upload a sketch, the IDE just gets stuck. On the board I have observed that the moment the IDE gets stuck the RX, TX LEDs stop blinking and it stays like that.
Any ideas how to trouble shoot either one of the problems ???
EDIT: I have tried the loopback test and both failed.