Hiw do I know that my Illinois tax return went through? It keeps saying I started it but I paid and finalized the efile return?

Yes, if your state return status says Started, rather than Accepted, it has not been accepted for e-file. To finish up:

1. Sign in to your TurboTax account. 
2. Check your return status on the first page. You should see a status for your federal return and a separate status for your state. If your state return status is anything other than Accepted, select Pick up where I left off, Fix my return, or Review.
3. If you see Fix my return, that means your return was submitted, but it was rejected for e-file. Follow the on-screen directions to make your corrections. If you get a message you don't understand, post it here and TurboTax can help you further.
4. If you status was Started, select State from the left menu, then State Review to begin the state review process. Address any details that come up. Once the Review is completely clear of details, Continue through the screens to do your final review, and e-file the return.