I can't find the specifications for that computer, so I don't know if it uses a standard size motherboard -- either mATX or ATX. From the picture, it appears to be mATX-sized. There is another thread, linked here
that suggests that emachines does follow the mATX standard:
Just to follow up on this post. I received my parts yesterday and everything worked perfectly! Apparently emachines does fully comply with the micro ATX standards. I would also assume this is true for any other T series as well.
This is for a eMachine T3612, though, so YMMV. Good luck!! Please report back on what you end up doing.