What can I do to get outgoing mail going again?
You first need to work out why it is not going.
"Can't establish smtp connection" means just what it says. If you have a "Smart host" configured, then that Smart host is no longer accepting SMTP (i.e. outgoing mail) connections from your server. Talk to your ISP.
If you do not have a "Smart host" configured, then your SMTP connections will be going to various places. If all those are failing, then either your Internet link isn't working (which I think you would have noticed and told us about), or your ISP has started to block outbound SMTP connections - in which case you'll need to switch to using your ISP's mail server as "Smart host".
If your server has been used to send spam, you should figure out why/how and fix that problem before you bother to fix the outdoing SMTP problem.