Where do you see only one CPU being detected- in the BIOS or on the POST screen or in the OS? If you see both CPUs being detected in the BIOS or on the POST screen but only one in the OS, then your OS either does not support multiple CPU sockets (any home version of Windows) or not set up properly for more than four CPU cores (if you rolled your own *nix kernel and set NR_CPUS.) Go into the BIOS and see what it says about what CPUs it sees. If you see both CPUs in the BIOS but only one in Windows, get yourself a suitable version of Windows.
If you only see one CPU in the BIOS, then the fact that you have swapped the CPUs and each one works properly when in the first socket means the CPUs are good. I'd bet one of the following being the cause of the second CPU not showing up:
1. Second CPU turned off in the BIOS. Go and turn it back on and it should show up. I actually doubt this is the case if you reflashed the BIOS, most boards default to having all CPUs turned on.
2. Defective socket/bent socket pins for the second CPU
3. Bad contact between the CPU and socket for the second CPU
4. Not having both the 8 pin and 4 pin power connectors plugged in
5. Defective power supply not supplying power to both the 8 pin and 4 pin connectors
The board is an LGA771 board and there were only two UP-only models made for LGA771, and they were rare- a single core ULV unit and one dual-core. Any quad core LGA771 unit is going to support DP operation.