更正下列句子中的语法错误并解释更正原因。
Me and her went to the store.
Corrected sentence: She and I went to the store.

Explanation: 

The original sentence contains a subject-verb agreement error and an objective pronoun error. 

1. "Me" is an objective pronoun and cannot be used as the subject of a sentence. It should be replaced with the subjective pronoun "I", which is the correct subject of the sentence.

2. "Her" is also an objective pronoun and cannot be used to describe the subject of the sentence. Instead, it should be replaced with the subjective pronoun "she". 

Therefore, the corrected sentence would be "She and I went to the store."