Does the washer fill with water when it gets to the rinse cycle?
If not the washer will sit there in the rinse cycle until it fills with water.
The rinse cycle uses cold water only. Start a wash cycle and select cold water to see if the washer fills with cold water during a wash cycle.
If you do not seem to have any cold water turn the water off and remove the 'cold' fill hose behind the washer. Look inside the water inlet valve to see if the screen is plugged up.
If so remove the screen and clean it. Be sure to reinstall the screen. While the hose is off I would also run some cold water into a bucket to flush the line.
If you have not cold water and nothing seems to be plugged you may need to replace the water inlet valve.