An I2C display will connect to analog inputs A4 (SDA) and A5 (SCL). Those pins are in the same places on the proto shield as they are on the Uno.
Edit: the below is for a 1602 (16x2) or 2004 (20x4) LCD character display with a hd44780 driver.
For an I2C LCD display to work, the I2C address and the I2C backpack to LCD pin mapping must be correct. If the library default settings for either or both are not correct the LCD will not work. You can try to figure out the right pin mapping and use an I2C scanner to find the address, but if you install and use the hd44780 library that is done automatically by the library.
To install the hd44780 library. The hd44780 library is the best available for I2C LCDs. The library is available in the Library Manager. Go to Library Manager (in the IDE menus, Sketch, Include Libraries, Manage Libraries) and in the Topics dropdown choose Display and in the Filter your search box enter hd44780. Select and install the hd44780 library by Bill Perry.
The class that you want to use is the hd44780_I2Cexp class. There are examples to show how to use the library. The nice thing about the hd44780 library is that it will autodetect the I2C address and the I2C backpack to LCD pin mapping.
In the examples, there is a diagnostic sketch that will help us to help you if you still have trouble with the display. Run the diagnostic sketch and post the results.
It seems that the shield does have the extra I2C pins near the USB connector as well as A4 and A5 as shown in the red boxes. A4 and SDA are the same electrically as are A5 and SCL.
