逗号不可以连接两个句子吗（如此用肯定是不对的吗）

I didn't wake upon time this morning, I even ran into traffic, and my bike was broken;therefore, I was very late when I finally got here.

这是我在网上搜索逗号与分号使用方法的一个例句。

但我记得逗号不可以连接两个独立的句子，那 I didn't wake up on time this morning, Ieven ran into traffic 这两个句子中间用逗号连接，不就错了吗？

I didn't wake up on time this morning, I even ran into traffic, and my bike was broken; therefore, I was very late when I finally got here.
黑体部分是三个并列分句，在最后那个分句前有 and 连接。即：A, B, and C。

假如没my bike was broken， and 就放在 I even ran into traffic 之前。