Nokia Ovi Suite has been superseded by Nokia PC Suite which, as you can see on the official web page, supports Nokia C2-03 devices. In order to use the Internet, download and install the program on your PC, launch it, from the Tools menu select Options and click the Connect to Internet tab:

Then, select your home country, your operator, and press OK. After that, all you need to do is to press the Connect/Connect now button. For further details, I recommend you check the second link from Google search engine.