Like Sphynx said. That folder should contain the disk image for your guest. Depending on what you picked during install something with an extension like vdi, vmdk, or vhd. That's just the storage used for the VM. Hopefully you haven't deleted or moved that. But that init> prompt is suggesting the boot loader can't find the bits necessary to boot the O/S, but at least that it found the boot sector. Another option you have is to boot a Linux distro from the "CDROM" drive and see if you can't repair the boot information. Or possibly copy just the BOINC files off of that "disk" if you can get access to it using that booted CD. But that's unclear due to your comment about thinking you may have deleted the optical drive. Although, even that's easy to recreate.

Another chance is to build a new VM under a different name, then attach the original VM's disk as a secondary drive to that one. Then you can copy the BOINC files directly to the new Guest when you're ready. Plenty of options, none of which are super easy to talk through without a little more time.