Why is 4.5GB of my 8GB of RAM not recognised?

You have a 32-bit operating system. Because of this, your computer can only address 4 GB of the available RAM. That means, no matter how much you can stuff into your board (or how much your board can handle (as that could also be an issue)), your OS will only ever be able to work with 4 GB of it. The only real fix is to upgrade to a 64-bit operating system.

The clue is in the screenshot you provided. You're running a 32-bit OS which will only support 4 GB of RAM:

You have a 32-bit version of Windows, which can only use 4 GB maximum, because 2^32 is 4294967296. Some of that 4 GB is used for other purposes, so 3.5 GB is about the best you can do without a 64-bit OS.

According to Microsoft, 32-bit versions of Windows 7 (which you are using) are limited to 4 GB of physical memory.