For a few months I had not been able to get YouTube to play on my home network. I tried about every thing that I read on the internet. Last week, I decided to flash a new kernel on my GS4, cleared dalvik and all that good stuff. When I rebooted, I noticed that I wasn't connected to my WiFi anymore. I checked my settings and found that my saved static address was no longer there, so I simply chose DHCP and connected with my password,,,,, now YouTube has been working ever since.
So, if anyone is having the YouTube problem, try forgetting your Wifi settings, boot to recovery, clear cache and dalvik, then try re-flashing your kernel or new one. Let me know if it works.
Hope this might help someone.