Can't answer why your computer says 32 instead of 64 other than to tell you you installed a 32-bit operating system, regardless of what you think you did.
Operating systems have to give memory an "address" (this is called memory space). Think of memory space as being a post office box. The post office has only so many boxes to rent, and if you put in more requests for boxes (install more RAM that it can allocated memory space to), it'll simply ignore the requests it can't fulfill (it won't provide memory space for all the RAM).
That being said, 32-bit operating systems only have 4GB of memory space. But RAM is not the only thing to use memory space. Your video card (and it's RAM) need to use memory space as well. Most USB devices require a certain amount of memory space. Hard drive caches, monitor caches, and other devices can also use a small amount of memory space.
So, when all those are given memory space, your operating system only has 2.99GB of memory space left for your RAM, so that's all it can use.