First thing, make sure you have two monitors... Totally worth it.
For computer engineering the most you will use will be programs like Cadence orcad, eagle or a similar PSPICE circuit simulation software.
These don't really require a ton of horsepower so the dual xeon setup isn't needed.
That said I would get a better cpu, a ssd, and 8-16 gb of ram, vs. what I would do for a gaming computer.
So a reasonable comp engineering setup for ~$1200:
CPU: i5-4670k - $230
Mobo: GIGABYTE GA-Z87X-D3H - $135
Memory: 8GB of DDR3 1600MHz (I like corsair or mushkin ram) - $58
PSU: ThermalTake SP-530PCWEU - $65
Case: Fractal Design Core 3000 (Unless you already have one you like) $70
SSD: Samsung EVO 256 gb - $179 (Go bigger if you can spend the monies)
HDD: 2TB HDD (Personally I like WD black drives, but Seagate works too) - ~$150
GPU: AMD R9 270x - $199
OS: Windows 7 Professional OEM $135 (also a good idea to make a small partition on the HD and install Arch linux and learn that as well)
Extras: SATA DVD-RW Drive - $20
Totaling it up we get $1240 Which admittedly is a hair more than the budget but these are just rough prices I pulled out, you should be able to find better deals than what I priced out.
Welcome to the secret brotherhood of the electrical engineers!