E-newsletter and mailchimp intergration not working

All day I have tried to get newsletter to work.
I set up API for mailchimp and API passed.
I set SMTP and bounce and this also passed.
Created newsletter but when i sent preview and test it says it was sent but it was never received in y mail. What else am I to do? Please help. I read previous threads and it appears this has been problem in past. One of the threads even told client to use another syso e-newsltter.ies int ttem Mandrill which I do not see how it