Do you mean burning AND processing? i.e. using Shrink for example to compress video?
Will make a huge difference. When it comes only to burning, any PC will do. I have two PCs dedicated mostly to burning and both are 4 years old machines, 1400 Mhz Athlon-based, and I have no problem whatsoever.
Now if you want to process/compress video files, that's another story, the more CPU the better. RAM doesn't have a huge impact (256MB will suffice) , but CPU does.