More than likely, it's your old P4 CPU that's not up to the task. Video decoding is primarily CPU intensive, and these days it's pretty much assumed everyone has at least a dual core CPU.
A new video card MIGHT help if you get one that's capable of doing hardware video decoding with Flash, but given that unit probably doesn't have anything more than PCI and AGP slots, you're going to be very limited in selection for video cards.
Personally, I wouldn't waste the money on a computer that old. Take whatever you were going to spend on a video card for this old computer, and get one of those set-top boxes everyone is making now days. Western Digital has something, there's the Roku, and probably at least a dozen more. You walk through a big box electronics store and you should see plenty of options. Several of them can stream content from YouTube and Hulu, along with some other sites, and you'll save a decent chunk of change on your utility bill that way too, plus they're a lot closer to "instant on" compared to an old clunker desktop from 2004.
My old computer, a 2004 Dell Dimension 4600 2.8 ghz, I put in a year and a half ago an 450 watt power supply, and several months ago I installed a newer unused 160gb hard drive and upgraded to 2.5 gb ram expandable to 4gb, and I had problems getting it to get on high speed internet, never used this computer for high speed internet like the newer one.
Anyway, I don'g have but onboard built in graphics card, the video on you tube and elsewhere is choppy, uneven, not like the smooth running on my new computer.
I surmize it needs a video card? capable of handling streaming video? Or is it this old computer is too old to handle streaming video properly. Maybe more ram? I mean, I would like to put the old computer in my living room to easily check out video based content, which is close to my kitchen, its pretty much worthless for that right now, doesn't make any sense to me, toher than obsolet viedo graphics. .