The answer is you can't send email to the wider world (on the standard SMTP protocol) if your ISP is blocking it - you would need to either work around the block, or relay your email through your ISP.
Port 587 (Submission) is used to send emails into your mail server, ie from an MUA (like outlook, thunderbird) to an MTA (Like postfix, sendmail). MTA's speak to each other on port 25 by default.
Your ISP is probably blocking port 25 to reduce the amount of spam coming from infected customers PC's. The answer is to either get them to unblock port 25, or set up their mail server as a relay so your mail server shoves all email to them. (Or, you could get a VPN and bypass your ISP's mail block - personally I don't like ISP's which block port 25, although I do understand the business case)
1Which mail server software are you using? Also, are you trying to relay all mail through a single external server, or are you trying to send mail directly to recipients over port 587? – user1686 – 2013-03-30T23:35:13.837