Okay, just so you are aware, when changing the motherboard from the Alienware one, you will need an new Operating System. Also, there are now three different sockets for the Core i5 CPU, they are not interchangeable (we would need to know which model of i5 to properly advise). Last, even the oldest i5 CPU is still a relevant processor and although the may be a (slight) advantage to changing the motherboard, I'm not seeing it.
Here's what I'd suggest, new case, new PSU and new graphics - call yourself good.
By "stylish case" you leave much to the imagination - since cases really are an aesthetics thing, I'll recommend you spend some time looking at various cases, give us an example of what you like/desire in a case, we can work from there
That'll leave ~ £400 for PSU and graphics
PCPartPicker part list /
Price breakdown by merchant /
Benchmarks
Video Card: MSI GeForce GTX 770 2GB TWIN FROZR Video Card (£228.00 @ Aria PC)
Power Supply: XFX XTR 550W 80+ Gold Certified Fully-Modular ATX Power Supply (£73.78 @ Dabs)
Total: £301.78