Question: I realized I start sentences with *the*, *he*, *she*, *it*, *after* and *then* all the time. So I'm starting to use verbs instead. Here is an example of something I wrote:

> 
> Erin left out a sigh. "Why am I thinking so much about this?"
> 
> 
> She decided to forget about the thing, and go lie on bed instead. Talking to herself had really made her tired; a little bit more
> and she would go crazy. She reached to her desk and grabbed her phone.
> Hearing Benjamin's voice would probably snap her back to reality.
> 
> 
> 

I remember having read about this long ago (but I don't remember if the author considered it good or bad writing).

Answer: 
Begin a sentence with a verb sometimes. See, I just did. Twice.

As others have noted, you're apparently confusing gerunds with verbs in your example. But that said, gerunds are perfectly good words and can be used to vary your sentence structure. 

I don't know where you were told that a sentence can never begin with a verb. Imperative sentences (i.e. commands) routinely start with verbs: "Go to the store." "Bring me the book." Etc. It's relatively rare otherwise in English, as the conventional structure is subject-verb-object, but it's not unheard of. "Thinking quickly, Bob leaped for the door." "'Leaving so soon?' Sally asked." Sometimes it's effective to use a non-standard word order for emphasis or to save an unexpected word for last. "Left in the middle of the night, he did." "Kill me they might, but they will never defeat me."

If you find that you are in a rut and all your sentences follow the same pattern, then, as Tylerharms says, I would definitely make an effort to consciously break the pattern. (Now that you mention this, I have to look at my own writing and see if I've fallen into this!) Of course one should avoid the opposite extreme, of trying so hard to vary your sentence constructions that you over-use odd phrasings.
I have pondered on this question for some time. My conclusion is this: providing the sentence makes sense to the writer and the reader, using the verb or the subject to open a sentence is fine. I don't agree with those who say that the subject should always come first. Writers are creative people. Rules are there for a reason, of course. It's redundant prepositions that writers need to be more aware of, in my opinion.