Since I could not make PostgreSQL work under Cygwin this time, here is another solution:

http://forums.devshed.com/t159166/s.html mentions http://pgfoundry.org/projects/pginstaller/ project, which is a native Windows port of PostgreSQL, version 7.5. There is a development version available. During installation, it is needed to do the following:

• create a user account for PostgreSQL server to use, i.e. postgres/postgres
• give it the right to "Log on as a service": > cmd /c secpol.msc
  you can test the account with > runas /noprofile /user:postgres cmd

Set the following environment variables:

• Add Bin and Lib paths i.e. "C:\postgres\bin" and "C:\postgres\lib".
• Add Data path - "PGDATA" as the variable name, and "c:\postgres\data" as the variable value.

And below are the instructions on installing under Cygwin, just in case. I must mention that the solution below did not work for me!

How to install PostgreSQL as a service on Windows, with CygWin

Postgres 7.4.3, Windows XP SP1

1. Install CygWin from the Internet
2. Add Cygwin's bin directory to Windows PATH
3. run /usr/bin/cygserver-config script to install the cygwin server
4. add system environment variable Cygwin=server;ntsec to Windows, or in /cygwin.bat (set CYGWIN=server).
5. Add
   set PGDATA=c:\programs\cygwin\usr\local\pgsql\data
   to cygwin.bat
6. start cygserver service on Windows
7. create "postgres" user account
   # net user postgres $password /add /fullname:postgres /comment:'PostgreSQL user account' /homedir:"$(cygpath -w /home/postgres)"
   # mkpasswd -l -u postgres >>/etc/passwd
8. grant "postgres" user "Log on as a service" user right:
   # cmd /c secpol.msc
9. install postmaster as a service:
   # cygrunsrv --install postmaster --path /usr/bin/postmaster --args "-D /usr/local/pgsql/data -i" --dep cygserver --termsig INT --user postgres --shutdown
10. Create the PostgreSQL data directory:
    # mkdir -p /var/postgresql/data
11.  Change ownership of the PostgreSQL data directory:
    # chown postgres /usr/local/pgsql/data
12. Start cygserver:
    # cygrunsrv -S cygserver
13. Initialize PostgreSQL (as the "postgres" account; ssh to localhost as 'postgres'):
    $ initdb -D /usr/local/pgsql/data
14. Start postmaster:
    # cygrunsrv -S postmaster
    or through Services window.
15. Verify postmaster is running:
    # cygrunsrv -Q postmaster
16. Connect to PostgreSQL:
    # psql -U postgres template1