The ISP does this to force you to pass email through their servers. The hope is that infected Windows computers will just try to open connections directly, and not forward the mail through the ISP servers. As noted in this story, that is not necessarily true.
So, now you find yourself unable to open connections on port 25, but you still want to send email. You could set up your computer to relay mail through the ISP's servers, as described in this earlier article, but that may not be convenient if, for instance, you're accessing the Internet at a relative's home, since they would have to give you their passwords for you to do that.
So, the first thing to do is to check that you can connect to your home computer on the ESMTP port number 587. Telnet onto that port number on your home computer, and if you get a response, then this technique will work for you.
First of all, you should already have set up relaying as described here. If you set it up a while ago, verify that your keys are still valid and haven't expired.
As we're discussing this in the spirit of a temporary work-around, we'll be editing the sendmail.cf file directly. First, of course, make a backup copy of your current sendmail.cf file, because you'll want to reset it to its former behaviour after you stop using this particular ISP.
Now, go into your sendmail.cf file and find the smart relay line. It will look something like this:
# "Smart" relay host (may be null)
DS
Change that line to indicate that you're sending ESMTP to your home machine. It will look a bit like this:
# "Smart" relay host (may be null)
DSesmtp:mail-host.example.com
Next, we have to tell sendmail that it is to use port 587 for outbound mail to esmtp smart relays. Locate the block in the sendmail.cf file that looks like this:
Mesmtp, P=[IPC], F=mDFMuXa, S=EnvFromSMTP/HdrFromSMTP, R=EnvToSMTP, E=\r\n, L=990,
T=DNS/RFC822/SMTP,
A=TCP $h
and change the last line to read:
A=TCP $h 587
That's it. Restart the sendmail program, and you should be able to relay all mail through your home machine using authenticated relaying on port 587.