From everything that has been said above, it is clear that this is an issue with your provider but it looks like they either don’t know how to correct it (reminiscent of BT a few weeks back) or they don’t care. If you can create a new account with them and it works just fine, that obviously points to something during their recent upgrade that has affected some existing accounts.
Unfortunately the eM Client application is not very tolerant when it comes to misconfigured servers, and there are a few that are mentioned on this forum. Looks like when the less secure port is closed later in the year, your server will be counted among those few that are not compatible with eM Client.
Best you move to another application now.