What method did you use to generate the key in Cygwin?
If I remember correctly - from the commandline
ssh-keygen.exe -t rsa
follow the prompts from there.
This is a really late reply but I'm interested to know if your problem has been solved. If not please check the Online Help for SSH Key Based Authentication.
For information, I am pretty sure that cygwin using the openssh key format. TD uses the cygwin key format, so it will not work without conversion. Fortunately, puttygen has the option to import an opensssh key and export it in putty format. This is how we handled it with openssh keys from various Unix flavours, so I suggest that you try this.
Yeah I solved it by using PuttyGen instead of openssh generated key. Works like a charm!