Your question makes no sense. (and you've obviously not understood what MR said either)
you've said yourself.... your email address is blocked, not your IP address, so it doesn't matter what computer you send the email from, if it's on the same email account it will be blocked.
It's a bit hard to elaborate further as you've given no details of what sort of email account you have, but forget about your computers or your routers IP address, they are almost certainly nothing to do with your problem here (unless you happen to run your own private email server at home).