I'm not particularly familiar with Linux Mint, but it must have a boot loader installed, so it should be trivial to configure it to use either of Linux Mint or Tiny Core... Without having spent much effort googling Linux Mint, it looks to me like it's probably using the grub2 bootloader.
Assuming grub2 is in use, there's probably a GUI tool in Linux Mint that will let you fiddle with the grub configuration. Unfortunately, I know -nothing- about that process as I go old-school and just edit grub.cfg with a text editor...
And I literally just today learned some of the ins and outs of grub2. I previously used grub4dos for many years and grub2 turns out to be nicer but the config files for the two are significantly different.
The end result you want is for grub2 to have a
menuentry either directly in grub.cfg or in some file included by grub.cfg, that looks something like this:
# The following assumes that the kernel ( vmlinuz ) and initrd ( core.gz ) and
# the tce directory are all in /boot/core11.1/ on the boot disk
#
# /boot/core11.1/ should be owned by root:root
# /boot/core11.1/tce and everything in it should be owned by tc:staff
#
# /boot/core11.1/tce can be empty at first boot - maybe even doesn't have to be there
# at first boot. I always create it because I usually copy some stuff into it.
#
# The below assumes that the kernel is in file vmlinuz. If that's not the case, you have a seriously old CD.
# Likewise assuming the initrd is in core.gz.
# the bit in quotes in the menuentry line is what will appear in the grub2 boot menu
# the --id value is how you specify the menu entry when setting a default or fallback menu selection
menuentry "core 11.1" --id core11.1 {
# I often keep a museum of previous Tiny Core versions on hand so each gets it's own directory
COREDIR=core11.1
# and each Tiny Core version can have either a 32 bit or 64 bit config so TCE might be either tce or tce64
TCE=tce
# CHANGE THIS value to the UUID of your boot disk ( use blkid /dev/sd?? to find it)
BOOTFSUUID="093a03df-90b3-4383-a3e7-798f63f377bd"
search --no-floppy --fs-uuid --set-root ${BOOTFSUUID}
# these two lines just keep the "linux" line from being absurdly long
WAITUSB="waitusb=30:UUID=${BOOTFSUUID}"
TCESPEC="tce=UUID=${BOOTFSUUID}/boot/${COREDIR}/${TCE}"
linux /boot/${COREDIR}/vmlinuz ${GENERALOPTS} ${WAITUSB} ${TCESPEC} ${BLACKLIST}
initrd /boot/${COREDIR}/core.gz
}
If you have over 4GB of RAM (probably not, on an old XP box), you probably want to use a 64 bit version of Tiny Core, which is probably not what's on that CD. 11.1 is the current version of Tiny Core, so I guess the CD isn't -that- ols. I was afraid you had a 4.x CD or some such.
Final thought: If the computer can boot from a USB stick, -please- configure a bootable USB stick and get it working first. You may need to fiddle with the BIOS setting to allow USB booting.
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