I can't promise Netflix (don't use it but from what I read it has its own set of issues), but I put a $30 HIS Radeon 5450 in an old Dell Pentium D Optiplex and it works just fine for streaming Amazon VOD, ESPN3, Hulu, Crackle, etc. It's hooked up by HDMI to a Yamaha AV Receiver, and then to a Pioneer Elite Plasma. The 3.0 ghz Pentium D is a little better CPU than the P4, but not much, and I doubt enough to make any difference.
Does your old Dell have a PCIE slot for a video card?