Recovery disks are usually designed to only install the operating system if it detects that your computer is the correct model. Changing the motherboard will likely cause the recovery disk to refuse to install the operating system image. There may be a way to hack it, but even if you manage to use the recovery disk, and the OS does not crash, it will not have installed the correct drivers for your new motherboard, so you will have to install them yourself.
Now, assuming the computer came with a windows operating system, you are entitled to install that version of windows on that specific computer as many times as you want. Your problem is that, unless you have a Gateway, Dell, or a few other brands, it probably did not come with an operating system disk, so you will either have to get one from the manufacturer, from Microsoft, or from a friend.
Let us assume that you are licensed for Windows XP professional. You need to get an XP Pro OEM disk, install professional, and then enter the XP professional license key that should be attached to your computer somewhere. Now, you just need to go to another computer, go to the manufacturers website, and download the drivers to a thumbdrive or cd, then install them on your computer. You will also need to install the drivers from the disk that came with your motherboard. Now you should be set. Keep in mind, that you will only have installed Windows. Any other software that came with your computer will not be on there, though you may be able to figure out how to install it from the recovery disk.