Start of any Cygwin application takes more than a minute on Windows 8.1 x64. It doesn\'t matter, either I\'m starting mintty from shortcut or
Eventually I found what causes this issue, but I'm still not sure why. Cygwin works for other people in same environment very well.
Cause: On the start of every Cygwin application it tries to get credentials as it is described in etc/nsswitch.conf file. For some reason, it takes a lots of time for my account as it contacts with several Active Directory domain controllers via LDAP.
Solution 1: You can save the current user and group in etc/passwd and etc/group files and set Cygwin to check them before Active Directory.
mintty.exe and wait till it opensmkpasswd -c and save its output to etc/passwd file (you will have to create it, output should be one line)mkgroup -c and save its output to etc/group file (you will have to create it, output should be one line)etc/nsswitch.conf and writensswitch.conf contents:
passwd: files # db
group: files # db
Now your Cygwin should start immediately.
Solution 2: There is special CygServer application, shipped with Cygwin, which can be started as an NT service or as a simple process (just run usr/sbin/cygserver.exe). It caches credentials and propagates them to every next Cygwin process while cygserver is running.
Add it to startup or start it before your Cygwin session and you're good — cygserver startup will take time, but every next Cygwin process will start immediately.
Is it your case? I want to share my investigation steps, so you could check, if your case is same to mine.
mintty and you will see its connections in netmon: 
mintty connections in the tree view on the left and TCP and LDAP frames on the right after selecting on of those connections.nbtstat -a 8.8.8.8 in command line (replace 8.8.8.8 by one of IP addresses from netmon).Going deeper: I'm still playing with etc/nsswitch.conf file to get local credentials or maybe cached ones so it will run faster without cygserver. But no luck yet.