Time Warner Cable

Here is my interaction with TimeWarner Cable:

1. Sign up for service
2. Immediately sign up for auto bill payment.  I try to have everything charged to my credit card so I can't forget to pay things.
3. After two months, I get a nasty letter from TimeWarner Cable stating that I'm behind on my bill.  I check my credit card statements and they haven't billed me.
4. I call the number on the nasty letter and get a busy signal. It is 2010, and I'm somehow getting a busy signal when calling a business. And not just any business; a business that really seems to want to be my phone company.  I call for about thirty minutes and continue to get busy signals.
5. I log into their (incredibly annoying and awful) site, pay my balance, and re-enroll in automatic payments.
6. After two months, I get a nasty letter from TimeWarner Cable stating that I'm behind on my bill.  I check my credit card statements and they haven't billed me.
7. I call the number on the nasty letter and get a busy signal.   I redial several times.  I finally get through, navigate the phone system to the point of "speak to a representative," hear a recorded voice say "no circuit" and the call is dropped.
8. Repeat.

How does one explain this kind of incompetence?