I've tried deleting the
.Xauthority file in both locations.
Maybe something went wrong before that, but you certainly aren't going to succeed after this. If you found this advice somewhere, and they weren't referring to some extremely unusual circumstance that doesn't apply to you, blacklist that source. Restore the
.Xauthority file on the client.
If you've lost the
.Xauthority file, you may be able to restore it from a running process or from a temporary file. I have no idea how to do it with Cygwin. The simple way that will work everywhere is to quit the X server and start a new one.
If you get the message “no xauth data; using fake authentication”, then remote applications aren't going to be able to display on your local server unless it's configured with security turned off. Without the security of xauth, anybody can spy on your X session and inject input if they can access the X server; depending on the configuration, they may need to be local users (in which case it isn't so bad on a single-user operating system) or it may be enough that they can open a TCP connection to your machine (i.e. they're in your local network, which could be anybody if you're e.g. using public wifi). If it used to work and no longer does, it may be because some missing security check was recently fixed.
Once you have a valid
.Xauthority file, open a shell and check that you can run local applications such as
gedit. From that same shell, run
ssh -X user@remotelocation and try running an X application. Either that will work or you'll get error messages; read them, and copy-paste them if you ask for help. If it doesn't work, run
ssh -vv -X user@remotelocation; the extra debugging output will give some information as to why it doesn't work.
Do make sure that the server allows remote X connections. With OpenSSH, the file
/etc/ssh/sshd_config or some other location depending on the distribution) must contain