Make sure your services are all started. Sending from the server would use SMTP. Receiving email from the server would use pop3 or imap. Make sure the services are still running on the server... Try webmail as well. Plesk can be a pain when it breaks or if something goes wrong on the install. What Operating System do you have it installed on?
Installing postfix will break it I am sure. You probably need to uninstall postfix before it will work. You might want to think about to contacting parallels or a managed service provider to get it fixed. Did you follow some how to when installing plesk?