Something has gone wrong and now we no longer have a Linux kernel (not even recovery mode) installed. GRUB is still there, but it runs the memory test.
How can I fix this? Everything I've looked at applies to 2010 or something silly.
This link should help:
Basically, boot from a 13.10 live CD, reinstall your kernel (after making sure you where it and the relevant GRUB2 modules are supposed to be.
Hard to say but I'd guess you screwed up your EFI business in GRUB and now its lost.