Thanks for the log.
Well, the bad news is that you seem to be double damned. First, VirtualBox cannot run 64bit VMs without hardware virtualization support in the host, a.k.a. VT-x, and your Intel Pentium P6100
CPU does not support VT-x.
Second, when I look up what on earth "Hortonworks Sandbox" is, there in the system requirements is virtualization support. That means that the sandbox is in effect a VM platform itself which relies on VT-x, and since VirtualBox does not reflect VT-x into the guest it can never work as a VBox VM. VMWare does
reflect VT-x into the VM (at least in some versions), but that's moot since your CPU doesn't support it anyway.
Sorry for the double bad news.
ps. Another minor problem, mostly irrelevant given the above but I thought I'd mention it anyway: the Hortonworks requirements says 4GB minimum, whereas you gave the VM 512MB, and in fact your host only has 4GB total fitted RAM. A bit of a disconnect there. Obviously you'd have to check the Hortonworks whether that 4GB figure is correct - it does seem high. I would assume that you only need enough RAM for whatever VM you run inside the "sandbox".