DIY game console ? there are not many projects out there on this subject, mainly because of the ammount of work and time you have to put into something like this.
Matt, the author of the DIY Game Boy, got over this issues and manged to get it done. The core of the project is an Arduino that controls all the other modules.
There is very little soldering requiered on this project as it’s mainly constructed using modules and shields. The source code is posted on the project page so you should have no problem on making something similar.