I would make two points about the bold section. First, you probably don't want to use present participle because what his parents "taught him to do" is "help others" (as opposed to "helping").

Second, the word "content" or "contenting" as a verb should have a direct object. That is, it should be followed by the noun that is being made content. In your case that would be "himself." In common use, "content" as a verb is often used to refer to one's self, but there are cases when it could mean to make someone else content. He tried his best to content the protesters. In that sentence, "the protesters" are the direct object.

See more examples here.

In your example, removing the present participle and adding "himself" would give you this:

help others and content himself with the life he led.

I would make two points about the bold section. First, if the part in bold is meant to describe what his parents taught him to do, you probably don't want to use present participle because what his parents "taught him to do" is "help others" (as opposed to "helping"). In that case, it should be separated with a colon or dash to indicate that it refers to what his parents taught him:

...what his parents always taught him to do: help others and content...

If, on the other hand, the part in bold is merely adding to the list of things he kept doing, you could leave it in present participle.

Second, the word "content" or "contenting" as a verb should have a direct object. That is, it should be followed by the noun that is being made content. In your case that would be "himself." In common use, "content" as a verb is often used to refer to one's self, but there are cases when it could mean to make someone else content. He tried his best to content the protesters. In that sentence, "the protesters" are the direct object.

See more examples here.

In your example, adding "himself" would give you this:

helping others and contenting himself with the life he led.