Did you try to follow the instructions in the message? Seems quite clear to me...
Intel VT-x is required for 64-bit guests, because it provides facilities for protecting the host OS from the guest OS. Since you don't need this protection when you are just running a 64-bit host OS, you can run a 64-bit host OS without enabling VT-x, as you have observed.
If you were able to install a 64-bit guest OS on this system in the past, then it is likely that Intel VT-x was enabled at that time. Some firmware fails to re-enable VT-x after resuming from a deep sleep state. If you are able to run 64-bit guests after booting your system, but not after it has hibernated, then you may need a BIOS update.
Please try to follow the recommendations in the message dialog. Let us know how it goes.