I broke my parent's fav (limited edition) lamp... they got mad at me... They didn't want. To forgive me.. I already said that I'm going to buy the new one.. but. They. Refuse it.. what should I do?

Life is like this... you can't MAKE anyone forgive you... in fact nobody is entitled to be forgiven. Forgiveness is completely in the hands of the person who would be forgiving another. Its something offered, its not something that is ever OWED to another.

A lot has to do with the circumstances of what was happening that caused it to be broken. I'm guessing you either did it on purpose (being angry) or you was doing something inside the house you were specificly told NOT to do... (like playing soccer) neither of which are really accidents.

And that lamp might have had significant sentimental value to them that you really don't comprehend.

I think the whole key to this is what you haven't told us about what happened, that made them as angry as it did.