I don't think you're gonna find one (a socket 939 mb) with a third PATA connector, I don't know of any and I think I'm pretty familiar with all the 939 PCIe boards available. SATA is current tech and the PATA are there mainly for CD/DVD drives and if you have an old PATA drive or two you want to hook up. If you've got so many that you need 3 connectors then it sounds to me like it's time to get a new SATA (they're actually pretty cheap if you ask me) and move some things off those drives and retire them to duty in another system for completely non-critical data, they aren't going to last forever anyway.
My suggestion would be for a DFI LanParty UT Ultra-D (has a fan but it's a quiet one) or the only fanless solution that I know of since the Chaintech NF4 board is no longer passively cooled, the Asus A8N SLI Premium. I own both these boards and both are excellent. Most any 939 board you get is going to have on-board LAN, sound and FW although there are choices without some of that.