To build a new computer, even reusing parts that you have now, you will need the following parts: a new motherboard, cpu, ram, and power supply. This is assuming you get a motherboard with onboard video, since your old agp video card won't work on any new motherboards. You could also just buy an inexpensive pci-e video card, if buying a board without video built in.
Power supplies have changed a bit since the A7N8X days. It would be best to get one with a 24pin connector, and more power on the +12v line than was normal back in those times.
Here is a mid level Core 2 Duo build (4 core for better video encoding times) with good parts from Newegg:
GIGABYTE GA-EP45-UD3R http://www.newegg.com/Product/Product.aspx?Item=N82E16813128359 $105 after rebate
Intel Core 2 Quad Q8200 2.33GHz http://www.newegg.com/Product/Product.aspx?Item=N82E16819115055 $150
G.SKILL 4GB (2 x 2GB) 240-Pin DDR2 SDRAM DDR2 1066 http://www.newegg.com/Product/Product.aspx?Item=N82E16820231166 $90
CORSAIR CMPSU-400CX 400W ATX12V V2.2 80 PLUS PSU http://www.newegg.com/Product/Product.aspx?Item=N82E16817139008 $30 after rebate
And a wild guess on what you'd need for a PCI-E video card. This one is HDCP compliant and has both DVI and D-sub connectors
XFX HD-465X-YAF2 Radeon HD 4650 http://www.newegg.com/Product/Product.aspx?Item=N82E16814150393 $50
You'll notice that the total is $425 after rebates. You can buy a Dell or HP for less, with a one year warranty. May not have quite as good a selection of parts, but it would be complete, with operating system and probably a monitor for that price. It is possible to go cheaper than the parts I've selected, but this is a slightly higher performance build than a bottom of the line machine.
I used Intel for this hypothetical build simply because I am more familiar with it now, and because they have a slight edge in performance in video encoding.