The VHD format is prone to this kind of failure, and for that reason should be avoided when possible. Deleting a snapshot would not have caused it, but running out of disk space while it was working would certainly do it.
So, first make sure you have lots of disk space free. Then I would try cloning the base VHD to VDI format. If VBoxManage doesn't work then you can try doing it with
CloneVDI. If either succeeds then you should be able to build a new VM around the clone VDI. If neither works then I'm afraid the only thing that can save you is a backup.
I also suggest avoiding the use of snapshots in future, particularly if you have limited disk space.