If I worked in 2016(Sept) but did not receive the check until the end of the year and did not deposit the check until January of 2017 can I claim zero income for 2016?

Basically it depends; The IRS allows TPs/small businesses to choose between the cash method and the accrual method for reporting income and expenses on their tax returns.
The cash method is the more commonly used method of accounting in small business. Under the cash method, income is not counted until cash (or a check) is actually received,so in your case you must report the income on your 2016 return as you said you received the check at the end of the year of 2016; if you use accrual method, you still must report the income on your 2016 return since your income is earned in the year of 2016.