Thanks for reaching out, and I'm sorry about the bumpy start with CE. What you've described is odd/unique; I would expect our blocker to block the whole email program rather than certain accounts. Let me encourage you to call our Support Team at 989.720.8000. They're based in Michigan and available until 11:45 pm (EST). They'll work with you to smooth things out, and they'll be faster than working through the forum. It's free as part of your subscription.
If you do want to continue working on it here, then please answer the following:
What version of MacOS is on the computer?
Is there a malware program on the iMac?
Are there any other accountability programs on the iMac?
Are there any other filter programs on the iMac?
I asked the last two questions because sometimes instead of helping each other, they'll fight each other in order to do their job. And a person, like you, gets weird side effects like odd/slow connections.