Node.js no longer works in Cygwin. The workaround is here.
This guide is working as of Node.js .10.16
Install Node.js from the msi on the site: http://nodejs.org/download/
Do not install it in Program Files
Install Console 2
Once cygwin is set up and you've installed any other necessary applications (e.g. vim etc), open Console 2 and select Settings > Tabs. Create a new tab (e.g. "Bash") and for the Shell: input set the following:
C:\cygwin\bin\bash.exe --login -i