Roughly 1600$ budget for own gaming

Hello,

I am fairly new to the forums and I am looking into building my own computer. I currently run a roughly basic (if not just basic) Dell dimension 5150

CPU: Intel(R) Pentium(R) D CPU 2.80GHz, 2793 Mhz, 2 Core(s), 2 Logical Processor(s)

Motherboard: Dell Dimension 5150 E510

Memory: 4gb (4 x PNY OPTIMA 1GB)

Video card: ATI Radeon HD 4670 1 GB 1024MB PCI-E Video Graphics Card (most proud of -.-')

and honestly do not know much more. I wish i did but if i could get help in building my own with a 1600$ budget or upgrading my current one. (personally, since it is so old i don't think that i can) thank you so much. I'm starting from scratch so any help would be appreciated!