Why don't my Game Boy Colors Games play after I install the backlight?

This is because the resistor was not installed. Install the resistor to solve this issue. The recommended voltage for all backlights is around 3V. The longer wavelength colors, such as red an orange, have lower voltage requirements so make sure to install the resistor.

I installed the bivert chip in my DMG Game Boy, but the screen contrast did not invert . All of the wires are perfectly soldered to the proper board points and chip pins. 

Make sure to cut the 2 leads on the PCB. Be careful not to cut any others or your LCD might not display correctly.

Why does my GBC flicker after installing the GBC frontlight? 

See here: http://handheldlegend.com/pages/flickering-gbc-frontlight