This will work:
Runs onboard Radeon 6310
The system is capable of flawless full HD (1080p) and 720p video playback. A Transformers Movie Trailer played via YouTube in both 1080p and 720p resolutions consumed between 29% and 37% of CPU resources. When played in Windows Media Player, the Coral Reef Adventure in full HD produced approximately 10-15% CPU load, while with 720p version it was between around 8 and 13%. In both cases the playback was completely smooth.Source
So that's case, mobo, cpu(apu), and a PSU, now we need memory:G.Skill 1066 DDR3 for $19.99
And we're up to $149.98, now the question is do you want to run an OS from a HDD? SSD? USB device? or "The Cloud" ( think Jolicloud)? Well that's your choice but personally I like to have some form of local storage regardless. I'd go with this here: 80 GB Re-certified WD SATA HD for $49.99
.Totaling now: $199.97.
With $0.03 to spare I would suggest you borrow a USB stick from a buddy (since $0.03 won't buy you much
) and follow the directions here
to install Ubunu from a USB device. I would say burn it to a disc and install it, however we've now met our $200 budget and cannot afford to purchase an optical drive.
I've now completed your challenge, what's my prize?