Have you updated the BIOS? If not please do so, and DO NOT USE @BIOS. It does support your CPU, it just may not have the latest BIOS which supports the 45NM cpu and so it may be acting like this because of that. After you flash you will have to load optimized defaults, save and apply, and reboot and make any disk changes you need before starting windows. Since you have already installed windows you will have only two options to correct windows CPU thoughts about your CPU. You can either do a clean install again, or try uninstalling the CPU from device manager and reboot and let windows reinstall it, that will likely put in the correct driver, but it may not I am not so sure
I just found here that your CPU while being 45nm is not supported, but it may still work you will just need to try the latest BIOS. If it does not work then you will need to buy a new board and return that one as E5200 is not on the Supported CPU list, the new 45NM Quads are and most of the E8XXX serires just not the CPU you have chosen >>>
GIGABYTE - Support - Motherboard - CPU Support List - GA-G31M-S2L
Some boards support CPU's that are not listed as being supported, but not always. Same applies for BIOS versions some work with CPU's they do not say they work with. So you best bet is to try the latest F6 or F5 and see if a clean install will get your cores working. If not you will have to decide on a new board.
You should have looked before you bought, not offense meant there just reminding you before you buy a board again always go to check the CPU support list
Here is some Flashing with Qflash Info
Flashing, here is some info on using Qflash. You can use 3 things with Qflash.... USB Stick, Floppy, or FAT32 Partition on your disk >>>
What you should do is manually download the correct BIOS for your board model and board revision from Gigaabyte Site Below. Extract the BIOS file you need, the .F# << # Being BIOS number like .F11. Be sure to choose the correct Rev. It is printed on the board in the bottom corner under the PCI Slots.
Here is your BIOS page >>
GIGABYTE - Support - Motherboard - BIOS - GA-G31M-S2L
The BIOS file you download is a EXE which is made just to extract to the Floppy drive or A: drive.
You can get the BIOS .Fxx (xx Being BIOS number and how the actual BIOS file extension will look) File out of this to flash with Qflash or DOS (DOS Flash files are also inside the Exe. by using winrar to extract the files.
Download Winrar Trial here (Scroll down to Winrar 3.71 and download) and then install and right click the BIOS exe file and choose extract here >>>
WinRAR archiver, a powerful tool to process RAR and ZIP files
Then you can either run any CD you have to get DOS loaded and use the files extracted. Or you can put them on a FAT32 USB drive and use Qflash. You may also make a new 1GB FAT32 partition on your disk if you like and keep BIOS files there as well.
To use USB you need Legacy Storage Detect Enabled in the Integrated Peripherals Page of the BIOS. You also need to leave the USB drive plugged in when you reboot to Qflash (Select "END" at bootup, or F8 Within the BIOS to enter Qflash)
Once inside Qflash you will be presented with Disks or Drives depending on what you have available, look thru each until you find your BIOS file and then flash it
Once you have flashed and rebooted back into the BIOS choose Load Optimized defaults and save and apply and reboot Back into the BIOS before you go into windows. You will need to set your hard drive settings again, especially do not try to load Windows if you are using a RAID setup without setting these settings again (Just have to say incase anyone is reading this for any board and is using RAID)
PLEASE DO NOT USE @BIOS!! << ANYONE READING THIS