http://ca.pcpartpicker.com/p/jjknZL
That's as CLOSE as I can get ($445 after rebate). It only has a 1GB video card, but it would still be a lot better performing than what you did have. Don't expect it to run every game.
*I simply couldn't go any cheaper on certain components, especially the POWER SUPPLY.
I also removed the DVD burner as there are ways around that (i.e. burning Windows to USB stick). Again, you have such a tight budget it's hard to do anything with it.
Other:
a) CPU is overclockable. Even on that motherboard you can probably get at least 4.2GHz.
b) 1x4GB can handle most games. Again, no shared VIDEO memory with a dedicated card. It's only operating at 800MHz but testing shows it won't make a big difference for most games with that CPU.
You should get an identical 4GB stick later (same model).
c) Better GPU recommended:
GTX750Ti 2GB or better (at least 2GB recommended).
*For your budget, I suggest investigating USED CARDS. Ideally one you can see working. Here's a rough performance guide:
https://www.techpowerup.com/reviews/EVGA/GTX_950_SSC/30.html
For example, the GTX950 at 1080p is rated at 100% and a default AMD 370 is rated at 80% of that. So the GTX950 on average is about 25% faster. The APU you got might not be on the chart at all (definitely not with a single, "1600MHz" stick).