in task manager you should see 5 or so postgres.exe processes. if you do, then the service is running afaik. no need to start the service again.
you can verify that its started by going to 'control panel -> administrative tools -> services' and finding PostgreSQL and seeing if it says Started.
try this:
start -> programs -> postgre -> pgAdminIII
double click your database server on the left pane, enter your db password. does this work? if it does, then your db is working properly, and its likely that PT3 is configured incorrectly, with wrong connection info or user/pass info. then you resolve that in PT3s Database Management window