Follow this to the “T” and make sure you get the right Hardware driver installed for your arduino. (Then I assume you’ll have to flash Marlin or some other printer control firmware to the arduino).
you need to get driver from seller and then uninstall the default one from windows i had lots of problem with mine printer you have to try lots of drivers
I have yet to see anyone mention just try changing the baud rate on say repetier host. In printer settings. Start with one end and work your way through the speeds till one works. Also is 1.6.1 the recommended version of ide for your firmware? I use 1.0.1 to 1.0.4 version of ide myself. Try multiple programs for speed communication adjustments. Windows ten will at times also cause an issue depending on what is on the USB chip that handles the communication with the 2560. Then also dbl chk what port your on. Try a few different ones, looks like you have done this already. If you have another Arduino board laying around, may be able to connect that way. I would try a different computer though just to make sure it’s not the PC in any way.
Hope you have tried a different USB cable and jack. Not just one. Also are you running a RAMPs 1.4 on a mega? If so, try using Arduino ide 1.0.4, should be able to see com port, set it, board type - Mega adk something, the programmer as ide. Also I know Windows has been adding support for the 3d printers and various boards. There are new options and features so that you can print direct like s printer and setup in a que. But usually it’s with higher price board like a rambo
I guess you fixed problem. No response lately. Hope it was just a USB cable. If on a USB dongle that may also cause an issue at times and may need to take it out the equation. Want as minimal things hooked up. Does board blink any LEDs when power is on?