Ok. First of all you've assigned too much RAM to the VM. I would reduce the allocation to 2GB.
VBox.log wrote:
00:00:05.512343 Host RAM: 8107MB (7.9GB) total, 3204MB (3.1GB) available
..
00:00:06.192209 RamSize <integer> = 0x0000000100000000 (4 294 967 296, 4 096 MB, 4 GB)
Also, you have a dual core host and assigned both cores to the VM, leaving none for the exclusive use of the host. This means that the VM has the potential to drag down the host. However you had better leave this for now until it becomes certain that its a problem.
Meanwhile, graphics RAM is far too low for any guest that uses a GUI. I'd increase to 64MB.
VBox.log wrote:
00:00:06.192478 VRamSize <integer> = 0x0000000001000000 (16 777 216, 16 MB)
Finally, we get to the boot section.
VBox.log wrote:
00:00:10.596638 VMMDev: Guest Log: BIOS: Boot : bseqnr=1, bootseq=3142
00:00:10.624928 VMMDev: Guest Log: BIOS: Booting from Hard Disk...
00:00:10.717411 VMMDev: Guest Log: int13_harddisk_ext: function 41, unmapped device for ELDL=81
00:00:10.728541 VMMDev: Guest Log: int13_harddisk: function 08, unmapped device for ELDL=81
00:00:42.447903 VMMDev: Guest Log: BIOS: KBD: int09h_handler(): scancode & asciicode are zero?
00:24:42.036205 Changing the VM state from 'RUNNING' to 'SUSPENDING'
This looks like a normal boot, and I note that the VM ran for 24 minutes after that, before being shut down by yourself. I'd say that you have a GRUB problem, not a VirtualBox problem (apart from all the problems described above). So if you fix the problems described above and still can't boot then I would ask on a Linux or GRUB forum. What you may have to do is mount the disk in another VM, and access the grub script to fix what's wrong with it. Typically what's wrong with it, if it ever worked and hasn't been corrupted, is that you cloned a drive, which changes the ID which GRUB is using to identify the boot drive.