Having more vram does not make a graphics card more powerful. If the gpu is too weak then you just have unused vram. 1GB is enough for high at 1080p, only a few top end games maxed like bf3 will need more or if you have a multi monitor setup. Neither of these gpus are even near the power you need for that. Many low ends cards have more vram to trick people like you who think more vram means more performance. The 5770 is ~50% better than the 640.
It says the max ram is 4gb simply because the pc came out before 4 gb sticks were available. It should have no issue upgrading to more ram but 4gb should be enough with that gpu and cpu.
BTW the case can handle full sized, multi slot cards unless you have something in the x1 slots. HP has been using that case for just about all of their mid towers for the past couple of years and still uses them for their current pcs. So it's pretty common to have topics made about it here.