Intel® Core™ i5-3570K Processor
In the above link if you go down to Advanced Technologies
VT is listed several times.
I believe this is the VT that counts!
Intel® Virtualization Technology (VT-x): Yes
Intel® Virtualization Technology (VT-x)
Increasing manageability, security, and flexibility in IT environments, virtualization technologies like hardware-assisted Intel® Virtualization Technology (Intel® VT) combined with software-based virtualization solutions provide maximum system utilization by consolidating multiple environments into a single server or PC. By abstracting the software away from the underlying hardware, a world of new usage models opens up that reduce costs, increase management efficiency, strengthen security, while making your computing infrastructure more resilient in the event of a disaster.
Have you tried to enable Intel VT-D Tech
in your BIOS and if so what happened?