You need to include more boot options.
like this
title Tiny Core
root (hd0,0)
kernel /boot/bzImage quiet tce=sda1 max_loop=256
initrd /boot/tinycore.gz
or this
title Tiny Core
root (hd0,0)
kernel /boot/bzImage quiet tce=sda1 home=sda1 opt=sda1 max_loop=256
initrd /boot/tinycore.gz
Change (hd0,0) and sda1 to the correct partition.
If you use the first one, you need to use backup. This will result in start up and shut down taking longer. However, the usb drive will last longer.
If you use the second one, you can have very little in backup, so it will be very quick. But the usb drive won't last as long.
My personal opinion: If you use it for browsing the internet, use the second one. If you don't use it for browsing the internet, use the first one. Internet cache adds a lot to backup. I think it is easier to buy a new drive when it fails (probably in several years time), than to waste time every time you start up and shut down.
This should get it working, but there is still more to learn. Read up more. Here is one example.
http://wiki.tinycorelinux.com/tiki-index.php?page=Backup