Well, it is hard to tell from your post exactly. Your host may have relay safeguards which could be preventing you from relaying your mail (such as POP-Auth, in which you'd have to check your POP account, right before you send it).
My ISP needs the:
Outgoing Mail Server: My server needs authentication
...checked or mail won't go through.
And another cause could be that your ISP blocks relaying, so no matter what you do, if it doesn't come from your ISP account, it won't go through. Even if this si the case, you might be able to work around it (sort of), by using your ISP's SMTP server and simply putting the return address as something else. This of course, is not sending mail through your server, but in case that's all you want (your domain name in the reply field), it works.
So we can't tell what the exact problem or restiction is, however maybe this will get you asking the right questions to your host/ISP.