Run postgresql in a background process.
Start a separate thread in your application that would start a postgresql server in local mode either by binding it to localhost with some random free port or by using sockets (does windows support sockets?). That should be fairly easy, something like:
system("C:\Program Files\MyApplication\pgsql\postgres.exe -D C:\Documents and Settings\User\Local Settings\MyApplication\database -h 127.0.0.1 -p 12345");
and then just connect to 127.0.0.1:12345.
When your application quits, you can always send a SIGTERM to your thread and then wait a few seconds for postgresql to quit (ie join the thread).
PS: You can also use pg_ctl to control your "embedded" database, even without threads, just do a "pg_ctl start" (with appropriate options) when starting the application and "pg_ctl stop" when quitting it.