Castor,
I don't have GMail so I'm not all that familiar with their service. But it seems that the primary problem here is the following:
"PERM_FAILURE: SMTP Error (state 9): 550 5.7.0 Your server IP address is in the SpamCop database, bye"
That is telling me that, somehow, your current IP is (or has been) used by a spammer at some time recently.
The first thing I would do is check your machine for spyware. Use AdAware, Spybot S&D, MS anti-spyware, etc. to see if your machine is infected. If it is, clean it up. If it isn't infected, then I'd call your ISP with a few questions.
1. Do you receive a different IP everytime you dial in?
With dial-up, most ISP's assign you an IP that is available when you dial in, so your IP will change each time you log on. But, from what I understand, there are a very few ISP's that will assign you the same IP each time you dial in. You need to find out how they do it.
You could test this by dialing in several times and then going to this address:
http://www.whatismyip.com/
If your address is the same each time you dial in, then your ISP has assigned you a permanent IP. I don't know if ISP's do this anymore but they used to do it. Now, if they do assign you a permanent IP, call the ISP and ask them for a new IP. That should get rid of the problem unless some spammer has figured out their IP range and has used most (or all) of them. But if that has happened they would know about it as many other people would have already complained to them with the same problem.
So try those suggestions and get back to us.