I have purchased an Intel i7 3770 and an Asus P8Z77-M Pro; for some Windows Server 2012 testing.
In the BIOS I have enabled the "Intel Virtualization Technology", and have several Hyper-V based virtual machines running.
I thought everything was fine; but hit an issue when trying to install Remote Desktop Services. It said that "Hardware Virtualization not enabled"...
I have installed a program called "Securable" which tells if the hardware supports it or not, and it comes up as "No".
Does this sound like an issue to return the CPU back for warranty, or would this desktop CPU really not have "Hardware Virtualization" ability? (All I can read on Intel's site says that it should.)
According to this link: Intel® Core™ i7-3770 Processor
It supports Hardware Virtualization VT-x
Most likely the issue is with the BIOS not enabling the Virtualization feature of the CPU even though it says it is enabled. My best guess is that you have and older BIOS revision.
I had a look through the website and full support for the i7-3770 was added in BIOS revision 1801. If your BIOS is older than this then although it may run it might explain why the VT-x feature isn't working. So the first step is to download the latest firmware which is currently 1805. Then see if it works.