Could you provide some more details on how you have your Arduino Breakout board hooked up to your PC? Sharing a picture would be great as well.
Also, what Edison devices to see listed in your PC's Device Manager (Start->Run->'devmgmt.msc') when connected? Take a look under "Ports (COM & LPT)". You're looking for a 'USB Serial Port (COMx)' and you want to tell Putty to use 'Connection Type: Serial' , 'Serial line: COMx' at 'Speed: 115200'.
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That's weird. Did you try to flash your Edison? If you aren't please follow this guide: How to Run the Flashall Script
After you have flashed it, please try to update the USB serial driver (the latest): http://www.ftdichip.com/Drivers/D2XX.htm
Then try to connect your Edison to putty using this guide: IoT - Setting up a serial terminal on a system with Windows* | Intel® Software
If you still have issues, could you please send us a photo of your Device Manager? Or try it with a different USB cable.
I hope you find this information helpful.
Have a nice day.