Hi,
Welcome to the forums.
Your CPU-Z pics show this Asus M2N is your motherboard:
Asus' specifications for your board state:
4 x DIMM, Max. 8 GB, DDR2 800/667/533 ECC,Non-ECC,Un-buffered Memory
Dual Channel memory architecture
The answer to your basic question is, yes, it should work (and much better) with more than 2 GB of RAM, but ONLY if you are running a 64 bit version of Windows.
The board has only two RAM slots, and it uses dual channel memory so you'd be better off buying 4 GB (2 x 2 GB) or 8 GB (2 x 4 GB) of RAM because your system won't operate in dual channel mode with 6 GB (1 x 2 GB and 1 x 4 GB).
If you are running a 32 bit version of Windows, the most RAM the system can access is a little more than 3 GB of RAM, and the best you could do would be to change one of the 1 GB sticks to 2 GB. You'll have more RAM, but you will lose the benefit of the dual channel operation.
Hope that helps.