So back to the beginning of computer design with Gene Amdahl (see the web?) where he said we needed about 1 million instructions per second to move 1 million bytes.

OK let's look at HD on Netflix to see how many bits per second we need.
https://help.netflix.com/en/node/306 gives us 5 Megabits per second.

A 5 MIPS CPU would be 8 to 10 times the power we need so how many MIPS in an old Core2Duo? http://www.maxxpi.net/pages/result-browser/top15---mips.php tells us 2,197.09 MIPS

-> So while it won't be speedy to run say Windows and browse, a simple box with say a dual core Celeron is more than enough.

15 Streams could be more of problem for the network. Especially if someone decides to try that over WiFi.