It may be that your IT department needs to whitelist Mailchimp's servers. The exactly URL depends on your API key that you are using to connect MailChimp to Chimpegration.
The API key often ends in "us1", "us2", "us3", etc
The URL that Chimpegration Classic uses to connect Mailchimp is of the following format:
us1.api.mailchimp.com
Clearly the "us1" at the beginning will vary depending on the API ending.
If you need the IP address that this corresponds to then do the following:
In the Windows start menu type in "cmd". Right click on the cmd program and select start as administrator. Once in the command window type in
ping us1.api.mailchimp.com
This will give you the IP address that the URL corresponds to.
Note that in the future other prefixes may be used e.g. uk1, etc.