Hey, I have seen cases with the 5830s where the plastic cover actually sits on the fan preventing it from spinning. Just in case I'd recommend you physically inspect that fan too.
I just built a new mining rig with 3 5830's on a ASRock 970 Extreme4 motherboard. Everything runs well but I'm having a strange issue with the temperature readings of the 3 GPUs. Every program I use only reports one of the card's temperature, it shows 3 different readings, but they are clearly pegged to that one card. Normally this wouldn't be to much of an issue, but for some reason, the fans on the other two cards will not spin up under load. The one thats sending the correct temperature works fine, but the other ones will mine fine until the temperature gets high enough that the computer crashes. These are NIB cards, so I don't think it would be because they were used previously. I have the latest CCC drivers installed, running Windows 7x64, using TRIXX and speedfan for readings, and GUIMiner for mining. Anyone ever had this happen?