Of all the questions I have ever asked in forums, I think that this is the most far-reaching.
The problem combination: 64-bit Windows Server 2008 R2 (May also apply to 64-bit Windows 7) with IE8 – the version you get with R2 or Windows 7. In a nutshell the problem is that Adobe Flash is not supported. Adobe's help line confirm it won't work. Anyone with an IE8 browser on a 64-bit system will get driven mad if they try to install Adobe Flash.
The solution is attention to detail, seeking the 32-bit iexplorer. It's in the Program Files (x86) note the (x86). Amazingly if you use this 32-bit iexplorer (even on a 64-bit OS), you can download the Adobe Flash stuff – YouTube will then work.
The downside. You will need to Pin the iexplorer in the Programs (x86) to your Taskbar or start menu to get the benefit.