|You will not find another model of motherboard that will fit in your case and is you could you would still run into other problems. Connections for the screen and drives, for instance.|
You have a dated entry level laptop with a 14" screen. It isn't worth fixing.
I suggest you put it on ebay for parts. Someone may need the screen or other parts.
Buy yourself a new up to date laptop.
Below is a link to your laptop specs.