Yes, you need to file a part-year resident return for each of the two states. WI can tax all your income prior to the move; IL can tax all your income after the move.
IL and WI have tax reciprocity for W-2 income. That means that the income you earned after becoming an IL resident is taxable only by IL.
In the Personal Info section of TT, enter IL as your state of residence. Indicate that you also lived in WI and enter the date you began living in IL. This will prompt the program to produce the correct state tax forms.
If your only income was your W-2 income, then answer NO to the question about having income from another state.