What dual core processor? Take your choice I've always been an AMD fan but Intel seem to be better value for money.
Do you need a good graphics card for playing DVDs and streaming videos? No, even onboard would do but I personally would go for one with a seperate graphics card even if its something like a lowely £40 GeForce 6200 as it stops you using the system memory for your display.
Regarding the soundcard, personally I would say no but decent speakers would. But a friend of mine is a musician and what I consider quite good he considers dreadful. Maybe I'm going a bit deaf but I can't hear the difference.
Assumming you get a Vista PC get dual core, preferably a seperate graphics card and 2 gig of memory. I personally think onboard sound is quite acceptable nowadays but perhaps you would disagree it depends how fussy you are.
And don't forget your monitor. If your monitor is poor and blurs the picture it makes no difference whatsoever how good the rest is.