I took a gander at the user manual.
Looks like that PC came with DDR2, so you'll need to get new DDR3 for that 4790K motherboard.
That CPU is among the most powerful consumer CPUs sold by Intel and is known to run a bit on the hot side, so you should monitor temps and possibly consider a replacement case fan.
Dell says your PC shipped in May 2008, so you've got a 7 year old power supply. Even if the existing power supply is compatible with your new motherboard choice, I'd seriously consider a replacement due to age alone.
Looking at a generic Dell Inspiron 530 manual, it appears that the 530, 530A, and 530C use a nearly square motherboard mounted with 8 screws. But the 540B and 530D use a narrower rectangular motherboard that has only 6 screw mounts. I assume you have the 530 proper, with 8 mounting screws, which would appear to be a standard ATX form factor. That's good.
I entered your service tag and looked at available spare parts. Dell shows no replacement motherboads; only RAM, hard drives, and processors among the major components.
Rough calculations:
CPU 340
New motherboard 150
8 GB DDR3 60
That's 550 for these required 3 pieces, ignoring the power supply.
I tend to agree with Bear--if you have to spend 550, why not go the added step of buying a new case for maybe 80 or 100 and a PSU for maybe 80? You'd have no worries about any proprietary complications of the Dell case and might well get improved build quality and cooling efficiency as a bonus.