Do you have both USB cables connected? There are two micro USB ports on the Arduino Expansion Board. One of them is the USB port used to upload Arduino sketches and to flash the Edison, and the other one is used to access the Edison's console. From the picture above, the serial port (Edison's console) is not connected (the USB port at the edge).
USB cables do wear, and it appears that the Intel Edison board is sensitive to worn cables. After I did every software thing I could think of, I finally just gathered up all of my Micro-USB cables I have gotten with Cell Phones, Battery Chargers, found, and so forth. After five cables, I got a connection?
So what changed in the Ports under device manager was that there were two COM entries, as shown in the image below. Before the cable changes, there were three entries related to Intel under Ports.
So my suggestion is to gather up every micro-USB cable you can locate, borrow or steal. Then switch out the cable from J3 or the micro-USB connector next to the edge of the board, till you see the USB serial port (COM#) line like in the image below, # is the number on your system.
Putty will connect upon pressing the Enter key.
You will need to close PuTTY each time you switch cables. The connector on J16 or the micro-USB connector nearest the small slide switch doesn't seem as sensitive, although I did have to switch the cable earlier on that one.
Electrical/Mechanical problems are always a disappointment when you just want to create software but this appears to be issue. If you have to, buy a brand new cable, in the package micro-USB cable, also, don't use the Micro-USB cables that have the LEDs in them (cool, but might be a problem). Just because a cable is new, doesn't mean it will work, but it has a higher chance of working.