The 4790 was a refreshed line. While it can be compatible with the same motherboard. It would have been up to Dell to provide a BIOS update to add support for the 4790. It may not be compatible.
If the CPU is broken. How do you know the motherboard is okay? Did it get physically damaged? CPU failure is extremely rare, almost unheard of. Outside of some external force which usually is accompanied by motherboard failure or a user tampering with overclocking.