For this to work, your machine must have a 'built-in' floppy drive and be able to boot from it.
(It stands to reason that this this method should not work from a USB floppy drive.)
If your (old) machine does not support USB-booting, but does have a floppy drive, then you need GRUB4DOS (Floppy disk - Bootable startup disk to launch the LiveCD, a USB stick, etc., from SliTaz Linux: http://www.slitaz.org/en/get/index.html).
Firstly, you will need to have your chosen distro - e.g. LinuxMint 10 - installed to a USB pendrive: there is a how-to for making a persistent USB key/pendrive installation using the Universal USB Installer, here:
Secondly, you will need a 3.5" floppy disc, formatted to DOS/FAT32 (they usually come preformatted to DOS).
Should you need to format the disc, in Windows (XP), 'right click' on 'Floppy Drive', select the 'Format' option, and follow the instructions.
To do this in Linux, you will need to install 'mtools' from the Synaptic Package Manager.
In Terminal, with the floppy disc inserted in its drive:
CODE: "sudo mformat -f 1440 A:" <enter>
(This forces (-f) the formatting of the disc to DOS/FAT32 with 1440KB space)
Thirdly, you will need to copy/write the 'GRUB4DOS' image to the floppy disc:
In Windows, this can be done with RawWrite http://www.chrysocome.net/rawwrite :
Run the program and follow the instructions.
In Linux, in Terminal:
CODE: "sudo dd if=/path/to/floppy/image of=/dev/fd0 bs=1440k" <enter>
e.g.: "sudo dd if=/home/slitaz/floppy-grub4dos of=/dev/fd0 bs=1440k" <enter>
(This instructs the operating system to write the exact file you specify to the floppy disc (/dev/fd0). If the path to the image file is entered incorrectly, then you will either receive an error notice, or the wrong file will be written to to the floppy disc, which will then have to be reformatted.)
Leave the GRUB4DOS floppy disc in its drive.
You are now ready to begin the process of booting from the floppy drive.
In the machine's BIOS manager, usually reached by holding down the 'DELETE' key on start-up, set your machine to boot from floppy drive and 'exit' to 'start-up'.
IMPORTANT: Have only the USB drive you want to boot from connected, otherwise the programme may try to boot any other USB device, e.g. USB Mobile Broadband modem, and you may have to start all over again.
When the GRUB4DOS page starts up, scroll down and select the 'Plop Boot Manager' option <enter>
Wait a few moments.
When the boot option page opens and the 'USB' indicator flashes <enter>
Wait a few moments.
When the start page for the distro (e.g. "Welcome to LinuxMint 10") opens:
Select a start-up option (eg "Start LinuxMint") and <enter>
Go and make a cup of tea (perhaps), or two: it does take some time, but it works, and it means that an old machine does not become obsolete, even when the hard drive dies.
Best of luck, and thanks for doing your bit for the environment!