I've played around a bit with 3D boards, but usually what I will find is that the 3D software requires a model of a component in order to view it in 3D. Eagle does have a plug-in to allow for 3D viewing, but it is rather limited. The software Andy provided is very nice, but I would imagine that the same pitfall prevails by limiting the components to a known database. The only reason why 3D would be nice to have is if you have multiple boards that sandwich between each other consuming the most volume possible. You did mention the creation of a cabinet to contain the electronic product(s). I would recommend going full out and getting a true 3D modeling software so that you can model the actual components one by one because chances are that the library of 3D parts is too limited to be useful. Solidworks or any other professional software without the bells and whistles of a mechanical engineer's dream would run about $4K US. That being said, there are a lot of free ones that can do exactly what you're asking, such as Google Sketch Up and a more comprehensive list via google.com:

http://www.freebyte.com/cad/cad.htm

Either way, I have always found that the 3D portion tends to be too time consuming to be worth the investment. I will generally find the tallest and shortest parts and neighboring space around them and try to match the volume with a 2D software. Eventually, I find that making a prototype is much much faster and guarantees good results, but I am paying for that speed.