不是病句.
因为主句要表达的是 medicine was the cause to something,
从句which并不是要补充说明cause,而是补充说明something.那，去掉TO可以吗你可以把which开始的从句替换成一个单词，来看句子是否仍旧成立。
medicine was the cause to recover. 如果把to去掉，就变成，
medicine was the cause recover.显然不对。
而recover的位置现在需要用一句话来代替，即
he could dedicate himself。
就成了原句里的medicine was the cause to which
he could dedicate himself.