You should always call Dell tech support and ask if there are bios updates that support newer CPU's. The same holds true for Gateway and HP as well. People here generally build their own and don't always have time to look up another person's OEM machine for support.
Regular motherboard manufacturer's always have a CPU support list for each motherboard that provides both the bios version and the board revision for each CPU. You check your bios version at boot (you might have to go into your bios to disable a brand splash boot screen), but you have to physically open your case to look for the board revision printed on the motherboard. Each company's web site has examples showing you where to find it, whether it's at the edge of a board or next to the CPU.
Dell wants to sell new PC's and seldom supports new bios for next generation CPU upgrades. If the motherboard's not too proprietary, you can have a standard motherboard with a new CPU and RAM installed, but then your operating system won't work, even after a reinstall, because OEM versions of Windows look for an OEM motherboard and bios.
I'd consider just getting a new case, motherboard, CPU and memory and transfer everything that works over. You can get an OEM version of XP or Vista when you buy the new parts at a store like Fry's or online at a retailer like Newegg.
You finally asked the right question when you asked whether a Pentium D 930 would limit a 4870. CPU limitations do happen, but they can be mitigated by gaming at a higher resolution. CPU bottlenecks occur when the CPU isn't powerful enough to handle all the frames pushed out by the GPU. That varies by game as well as by gaming resolution. Some games are CPU bound while others are GPU bound.
What monitor resolution are you using?