What follows are my own thoughts.
Some time ago, well, many years ago, I own a Gateway. The computer power supply went out and get wasted. They sent a new one.
And after that the machine continue to work for one quite a while, and I eventually sold to somebody else. But I will not recommend Gateway to any. The reason is that the dream of Gateway has faded, and now the company is simply going out of business. Unless they come up with a very clever way to keep a small group of happy customers, they will have to drop out of the business and go do something else. Maybe they could go back to raising milk cows.
At the present time, the major desktop computer companies are Dell and HP. ket. Also, you have to factor in two or three other companies.
Most of the computers I have now are Dell computers that I purchased refurbished. I have also had Compaq, IBM and HP computers.
Now if you are satisfied with the monitor you got from Gateway, you could go by a refurbished computer from Dell for less money than what you would pay for a new motherboard and CPU. You can get a i3 computer refurbished from Dell for less than $300 and it will come with a HD ram & warranty. All you have to do is that a monitor, keyboard and the mouse. In my opinion, that would be a better investment than trying to find the motherboard that fulfill the case of the Gateway computer. As for the hard drive, you could use an extra hard drive for backup. If you pick the right case, you'll be able to put another hard drive in the same case, and thus have extra storage space and the foundation for a good backup plan. Unfortunately, the power supplies used in many Dell computers have a strange form factor and then not going to work in another machine and vice versa.
So, simply put, my opinion is go out and buy a refurbished Dell computer and just use the leftovers from your Gateway.
It's just too hard to try to match up the CPU and motherboard, unless you're really deep into hardware. I've been doing hardware for a long time, and I get messed up myself find get the right CPU and the right motherboard. So I quit trying. Of course, that's just me. Maybe you'll do better.
BTW: A good refurbished desktop comes with a current version of Windows.