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Although there aren't any dual-core processors for socket 478, you can buy Pentium 4s with Hyper Threading (1 core, 2 threads) at 533MHz, but I can't guarantee compatibility. Consider the Pentium 4 3.06 GHz (Northwood), the only hyper-threaded CPU operating at 533 MHz. I'd advise you to try your luck because some users of the same machine as yours are successful in booting with the 3.06GHz CPU while others are not. The greatest choice you have if you can't tolerate that CPU is a single core Prescott 2.8GHz Pentium 4.
First, download the most recent BIOS update from Dell, which is available here. That resolves problems that some CPUs had with the D1 stepping. Choose the BIOS update installation method you like, then carry out the update (you can even download the .exe file to run within Windows to update BIOS; if you select this method ensure all other programs are closed).
Once upgraded, give the P4 3.06GHz with HT a go. It might work for you, especially following the BIOS upgrade, I have a feeling. If not, the P4 2.8GHz is your best option, as was already said (Prescott). I know this is off-topic, but I actually own both of these CPUs.