To me, "motherboard died" means to me is when the power button is pressed, no electricity is flowing besides the stand-by power. If you have fans turning, then the motherboard didn't die. Some other component is not working or is not seated properly. You have to inspect what it is. This is important if you want to get a replacement. If the CPU is at fault, buying a new motherboard will be a waste of time and money. If you have an OEM license of Windows 7, buying a replacement motherboard that is different will not work. OEM license are stuck to the motherboard. A retail license gives a little more options.
Do what Slosh suggested. Also remove the graphics card if you have one installed.
You should plan soon to upgrade to Windows 10. Microsoft is dropping support for Windows 7 next year.
Latest processors are able to run Windows 7. Microsoft just put a soft block for auto updates on the latest processors. It's possible to manually install Windows 7 updates for these processors. Motherboard manufacture won't support Windows 7 for the latest processors. This means there won't be any drivers from Windows 7 when using the latest processors.
What is the reason why you want to stick with Windows 7?