I found the answer to my solutions in this blog post.
"First locate the file called passwd
in your C:\path\to\cygwin\etc
directory and open it with wordpad. Second, replace the text /home/YOUR_NAME
with /cygdrive/c/Documents and Settings/YOUR_NAME
Finally, save the file."
Update
Some people have reported that adding %USERPROFILE% as a value to a system variable called "HOME" works.