It's a very interesting story, but right now that's what it is, a story. For a strong personal statement you need to maintain a singular focus throughout the entire piece. In the middle of your PS you switch from talking about your musical instrument (very cool I might add), and business, to discussing the death of your father. I don't mean to be harsh but right off the bat you should cut this:
During most of my academic career I had helped take care of my father. In my first year of college he became terribly sick, and doctors at The Mayo Clinic determined he had a rare disease. They gave him medicines for pain, and said that he would probably die within five years. We lost our family home and he has been surviving on government assistance since then.
In one of my sociology classes, I learned that families often alienate disabled or chronically ill members. In this way I saw my family ostracizing my father. I determined that I would keep him included in family activities and provide him with my own help. That task proved emotionally taxing and time consuming, but very rewarding. Over time, he was able to reintegrate into our family. Also, during the fall of 2007, my sister began learning how to help take care of him. By the winter of 2008, I had moved out of my role as a caretaker, and could fully pursue my own goals.
It's interesting and it says that you have a strong character but it's a topic all by itself. You could write a PS about this and how it impacted and changed your outlook on life, but I don't think you can add it here. So I would leave this topic behind and stick with your entrepreneurial endeavors.
Another thing I would mention is to cut down on your "wordiness". Go through the statement line by line and ask for each sentence, "do I need this?" or "how can I say this better?"
Also, all of this:
However, Taiwan was not what I expected. I was not prepared for the difference in business culture that I found in Taiwan. The Chinese concept of "Keeping Face" may have originally been to help relationships flow smoothly. However, in my experience, it often results in an ambiguous confrontational style. If my manager did not like what I was doing, I would usually find out from other people. And when I did find out that something was wrong, I had to guess what actions my manager desired of me. After living in Taiwan, I have come to cherish American directness.
Shortly after I arrived, the poor economy in America flooded Taiwan with English teachers seeking jobs. Wages dropped and I, along with most foreign teachers, went from having a surplus to merely subsisting. With little available cash, I could not refile my patent application when the examiner denied it. Moreover, as I queried about electronics manufacturing in Taiwan, I discovered problems. Quality control in Taiwan can be very bad. Being bilked outright is also common due to inadequate government regulation. I decided that I would prefer to manufacture things in a Western country.
On the other hand, my experience teaching was wonderful. Over time, I learned ways to find out what I needed to know from my managers, and to present issues so that everyone involved could save face. I enjoyed contributing something meaningful to my students. Also, I lived in a small town, and as a teacher I felt like I was part of the community.
...needs to go. Most of this is extraneous information. Extraneous information kills a strong PS. All of this can be boiled down to one 4-5 sentence paragraph - if that.
A strong personal statement IMHO should allow the reader to completely understand where you're coming from and your focus should be unwavering throughout the piece. I learned more about Taiwan in your article than I did about you, that needs to change.
I like the entrepreneurial angle, it really works. I would run with that and stay focused on only that topic. Also, my belief is that a PS has no business being longer than 2 pages. There's no excuse for a long PS, no matter how interesting your story is.
The best advice I received for writing a PS came from an admissions officer:
"This is our only opportunity to hear about you in your own words - the floor is yours."