Have a look in the event log application in Kentico. You may see some exceptions logged against the translation service. When you try to configure it for your site, Kentico will try to validate the service. If something goes wrong in that check, then an exception is thrown into the event log and the warning you are seeing is shown.
As an example, i just put nonsenese values in the settings (as i don't have an account) and I se the same warning:
This service is not available on current site, please check service settings in Settings -> Content -> Translation services.
If I look in the event log however, I see this:
The translation service returned the following error:
Message: Url 'https://www.mattnield.co.uk' incorrect or unsupported PD version (needs to be 4.18.0 or higher).
So it looks like - as you noted - the account settings you have need to be absolutely correct in order for the service to ba available. I don't know TRanslations.com particularly well, but it's worth checking things like IP whitelisting etc. too to make sure that traffic from your webserver is allowed.