open the terminal and type
sudo editor
Open /mnt/sda1/boot/extlinux/extlinux.conf
If not using sda1, use the appropriate partition.
in the line beginning with
APPEND initrd=/boot/tinycore.gz quiet
include the bootcode.
Then it depends on which options you chose when installing Tiny Core.
It may be syslinux, instead of extlinux. If you look, you should find it.