Getting pissy with the CS rep who you're talking to on the phone isn't going to do any good, and is really rather odd considering it's not their fault that you're having a problem to begin with.
I had a situation like that last October when I was trying to get my account signed up for the annual pass. It was telling me I was ineligible for some reason, so I opened a ticket and they told me I had a chargeback on my account so it was in negative standing. Confused, I call. Long story short, she told me even if I paid off the negative balance I wouldn't be eligible. This, obviously, pissed me off, but I knew it wasn't the rep's fault. I remained calm with her and told her that I'd like to pay off the balance anyway. So I gave her my card info, she paid it off, I thanked her for her time and we hung up. A few hours later I get a call from Blizzard's CS department, and the woman on the other end says she did some more digging and found out it was due to an account breach that happened when I wasn't even active. She apologized, acknowledged that it was unfair that my account had this negative standing to begin with, flagged my account as eligible for the promo, and offered to refund the money I paid for the chargeback. Signed up for the annual pass right after that. Okay so I guess that wasn't all that short.
Anyway, yeah, being calm and collected can go a long way. They may do customer service for a living, but they're still human. They're gonna get defensive when they're yelled at, especially for something they have no control over.
Heck, this goes for real life too! My mom went out of state to a job, and of course she had to rent a car. When she got to the car rental place early in the morning, she found out that they had no cars even though she reserved one. The computer system was still letting people make car reservations even though that branch didn't have any available. My mom had to sit at the branch waiting, since she had no way to get around anyway. Countless people came in and proceeded to yell and complain to the guy working the counter, even though it clearly wasn't his fault. Eventually, someone pulls in to return a car, and the employee looks at my mom and says, "See! Here's your car! I told you I'd get you a car, and here it is!" She ended up getting upgraded from the dinky little compact she reserved to a mustang. Patience and politeness go a long way.