First, don't listen to anyone who says upgrading a Dell is impossible. It can definitely be done, but it takes a lot more work than simply buying a new modern case and screwing stuff onto it. This is a job that requires metal cutting tools (Angle grinder, dremel tool or just snips) and lots of superglue. It's basically a hack job, and probably not worth the time and effort unless the case holds some sentimental value for you.
I recently upgraded my girlfriends C-521 with a new mobo and i5 2390T processor. I used an Asus P8-H61 mini itx motherboard. They are small enough to position up by the I/O ports and if you use the metal shield that comes with the mobo (and you don't hack up the opening too bad) it'll look nice and clean from outside. You'll have to mark the positions of the standoffs for the motherboard and mount them (you'll probably need to make spacers to "lift" the motherboard to the proper height so that it lines up with the I/O panel). I used a lot of superglue for this.
The panel for the Video card is on the bottom of the case and wont line up with the motherboard. So, for gaming, you'll need to get a long (12" or so) PCIE ribbon extension and run it from the PCI slot, over the motherboard and down by the opening in back of the case. If you are using a low profile GPU, it should fit in there pretty nicely. There are other options if you want to use a larger card, but they're a little more complicated.
Lastly, you'll need to buy a bezel wire pack for the front panel, plug them into the corresponding pins on the mobo and figure out a way mount the power switch in a way that doesn't look too janky.
The only reason I went through this whole procedure was because the PC was a gift to my girlfriend from her aunt who passed away and she couldn't bear to get rid of it. If you're just trying to save money, you might actually spend just as much going this route (if you factor in the cost of the wires, standoffs, glue, PCIE ribbon and so on) as you would buying a new, cheap case.
But the choice is yours. Good luck either way.