As you found out earlier, the exim processes are running now, which indicates that the server is ready to accept or send messages. If it is still having trouble then you should find the error message in the corresponding log of the mail server. once you have found the same, please let us know so that I can guide you better.
You can try checking the spamassasin configuration and also try reinstalling the same. You can also clearing the eximdb or try the update on exim. If you have any trouble that will include tech information. you can PM me or send me with message via forum or chat.
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You have specific scripts that will help you update the spamassasin configuration and also the exim update can be done quite easily. If you are finding it difficult please contact either via PM or mail.