According to my calculations there would be no light so the plants and animals will freeze to death.
The weather will always be cold and there will be no more sunlight.
The earth will melt
We would warm up and die as a planet.
A more relevant question would be what would happen to Earth's hydrological cycle if precipitation stopped. For there to be no more evaporation, our sun would have to die. If the Sun died, so would all plant and animal life...eventually...including us.
We would be dead because we cannot survive without the sun's light and warmth for more than 8 or 9 minutes.
The sun would win.
It would melt.
Nuking the sun is not possible with current technology. However, theoretically, if it were possible, the sun is so massive that a nuclear explosion would have negligible impact on it. The sun's nuclear fusion reactions are much more powerful than any man-made nuclear explosion.
It is very unlikely to the sun will every cease to rise. It is more likely that the sun would first cease to exist, most likely by exploding into a supernova. This would kill all of Earth's inhabitants.
You would be vaporised long before you actually reached the sun.
death
It cannot happen, but if it did we would all die shortly therafter.