首先，它是一个简单句，不是复合句，也不是并列句，因为句中的he being ill只是一个用作状语的分词短语，句子只有一个主谓结构，所以它是简单句。
其次，这个句子不能改为：He was ill, we took him to the hospital. 因为这样一来，它就成了两个句子，但句子间却没有相应的衔接方式，所以就错了！
为什么会错了呢？看上去好像很对啊！注意，英语句子从结构上看，只有三种类型，即要么是简单句(只有一个主谓结构)，要么是并列句(句子之间应有并列连词)，要么就是复合句(有相应的主句和从句)，除此之外，不存在其他的句子类型。He was ill, we took him to the hospital.这个句子的错误就在于，它既不是简单句(因为它有两个主谓结构)，也不是并列句(因为句子间没有并列连词)，也不是复合句(句子没有体现出主句和从句)。所以如果我们将这个句子改成以下形式则是完全正确的：
正：He was ill, and we took him to the hospital.
正：He was ill, so we took him to the hospital.
正：Because he was ill, we took him to the hospital.
正：He was ill, so he was taken to the hospital by us.
正：Because he was ill, he was taken to the hospital by us.(www.hxen.com)
为了帮助大家理解，我们再举几个例子来看看：
That day being Sunday, we had no classes. 那天是星期天，我们没有课。
that day being Sunday为独立主格结构，其中的that day为现在分词being Sunday的逻辑主语。如果要将being改为was也可以，那句子就必须处理成并列句或复合句，比如：
That day was Sunday, and we had no classes. 那天是星期天，我们没有课。
That day being Sunday, so we had no classes. 那天是星期天，所以我们没有课。
As that day was Sunday, we had no classes. 由于那天是星期天，所以我们没有课。