Hi, welcome to phpBB.com!
phpBB has set the e-mailing settings the to default phpBB mail() function by default. Those use the default settings that your host has set for them. If those don't work, you would need to add the SMTP settings that your host should supply. The fact that other applications have trouble does signal that this is not a problem but phpBB but rather with the server configuration.
I would recommend to re-contact your host and ask for the SMTP set-up details that would be required. If necessary ask for level two support so you get someone that knows what they're talking about.