First off, excuse my ignorance, but I'm new here and I'm really new to technology and as far as recognizing part names. I have a emachines t4892, more like a project for me, and the video part that is solder onto the motherboard is broken. I want to take that one out and put in a new one. Problem I'm having is finding this piece, and i really don't know the correct term for it. I'd appreciate any help I can get.

You could just use the AGP 8x slot on the Motherboard and put a video card in that
Note: AGP 8x is also very old technology now, but if you find an old AGP Video card it may just work

You can also chat with eMachines Support, to work out what part you are talking about: