Every ISP that offers usenet should allow posting (but will disable it if they get a complaint). At least text posting, at a minimum. Have you talked to them, and what exactly did they say? (I'll assume you didn't reach that conclusion after trying to post to a group they don't carry) A little more explanation would be welcome.
I know that on a few usenet providers such as Newshosting, users had to specifically request posting priviliges, as this was not automatic. An ISP could possibly be set up the same way, but that would be weird.
Also, if you live in the USA, it could be risky to post copyrighted files through your ISP. For one thing, many ISPs inject your IP address in the header info field, and even if they don't, just being identified with an American ISP makes you stand out as an easy target. (and many ISPs in the US have been known to rat people out without even a court order) For comparison, a post made on Astraweb, for all anyone knows, could have been made by someone living in some far-off country like Pakistan or Turkey, putting that poster (even if identified) well out of the reach of the Hollywood copyright cops.
Regarding Blocknews, it seems that it might not allow posting on a very new account. I could read messages and download files immediately after getting a Blocknews account, but all posts (both text and binary) would fail. But then the next day, everything worked fine, and has ever since.