You answered a lot about your topology when you said that you are sharing your landlord's wireless as do the other tenants.
When you visit
http://checkip.dyndns.com, does it display the same IP address as the one that the "client host (IP Address) is blocked" nastygram is giving you? If it is, ask your landlord to power down his modem for about a minute, then turn it back on.
http://checkip.dyndns.com shows the internet address of your landlord's network, that the rest of the world sees you (all) as. The router does what is known as network address translation, enabling multiple users to share this one externally visible IP address. Most routers assign local computers an address starting with 192.168.x.x or with 10.x.x.x. Some assign an address in the range of 172.16.x.x through 172.31.x.x. These addresses only have meaning on the landlord's local network. Yours is visible to you in System Preferences, Network, TCP/IP. The landlord's router keeps track of the details of playing traffic cop for the internet traffic of all his tenants, directing it to and from the correct computer, and you all share the one single externally visible IP address. It is likely that this address (the one seen by the outside world) is assigned dynamically by his internet provider, and cycling the power as described would likely assign a different address, that the outside world sees you (all) as. With a new externally visible address, that would likely clear up the problem of you not being able to send mail because the current IP address (the one seen by the outside world) was blacklisted as being a spammer on some list that your email provider for this specific account checks, and a different address likely would not be blacklisted (unless the landlord's ISP's entire domain is blacklisted - in which case, your landlord needs to advise his ISP about this).