Cheap build for general use (Not gaming)

Hi everyone, I am looking to build my parents a system to replace their old Gateway that is borderline useless now (after like 9 years).  I need all new hardware. But I NEED a quiet case because they want something almost silent.  

Where do you live?

New York City

Cheap low powerd fast pc for every day use no need for a video card there is intergrated video from the chip (there is allso on board video too)

It shude stay cool and quiet

CPU: Intel Core i3-3220 3.3GHz Dual-Core Processor ($113.99 @ NCIX US) 

Motherboard: Asus P8B75-M LX PLUS Micro ATX LGA1155 Motherboard ($69.99 @ Newegg)

Memory: Corsair Vengeance 4GB (2 x 2GB) DDR3-1600 Memory ($39.99 @ Newegg)

Storage: Western Digital Caviar Blue 500GB 3.5" 7200RPM Internal Hard Drive ($56.68 @ Amazon)

Case: Fractal Design Core 1000 USB 3.0 ATX Mid Tower Case ($40.04 @ NCIX US)

Power Supply: Corsair Builder 430W 80 PLUS Bronze Certified ATX12V Power Supply ($44.98 @ Outlet PC)

Total: $365.67

Problem solved.

Nice price but a 1.6 amd is going to be soooo slow 

I doubt they'll be making a 3D video, xD!

I had an Intel Atom in a laptop, worked well enough for browsing the internet...

I would rather have the Intel. But if worse come to worse I would go with at least 2.5 ghz AMD duel core cpu.  I have had a few bad experiences with the lower clocked ones being unable to even be remotely capable of even browsing the interne or watching videos.  

They do burn and make dvds for backups of movies and home movies

Optical Drive: LG GH24NS95 DVD/CD Writer  ($17.98 @ Outlet PC) 

Got a new disk drive in the old computer already so that's not necessary.