If you are trying to send mail from an AOL account (i.e. (e-mail address removed)) then have a good root around at
http://postmaster.info.aol.com/ to double check all your necessary settings for outlook express.
However, if you are trying to send third party mail (i.e. (e-mail address removed) or (e-mail address removed)) then your options are very limited.
AOL are the first of the ISPs to close down regular mail through port 25. It used to be rate limited but AOL's port 25 is now completely blocked off. Even worse, although you can use authentication on port 587 this only allows you to send mail from AOL accounts.
Looking at your error message, I could be wrong but this appears to be your problem: You've authenticated your AOL account correctly using the outlook express settings but the server is still rejecting your mail because it is not actually AOL mail.
If this is the case, what can you do? Not much, unfortunately. There isn't much sense in changing ISP because the rest are planning to follow AOL's example which is admittedly effective in the war against spam.
Hopefully, your business ISP have an SMTP server which supports authentication. Ring them and check. If so, you can replace the AOL SMTP server details altogether. Sadly, many ISPs don't have a server which supports authentication yet. If they only have a regular port 25 server, then this is *not* an option because port 25 is completely blocked via AOL. Worse still, many web hosting companies rarely have an SMTP server in the first place (not unless you are exclusively tied to their webhosting package with integrated broadband/dialup).
I'm in exactly the same boat with AOL myself and after 6 months of banging my head against the wall, I have chosen to use a gmail/googlemail account. You can configure these to work with outlook express over an AOL connection because they use are SSL servers (you are effectively using outlook express to collect web based email).
Not great news I know, but I hope this post helps!