I had trouble booting several distros on my newer computer. I think the trouble with mine was the sata cd drive - but it could have been other things that the kernels/different distros weren't able to automatically deal with.
I'm assuming your boot cd is ok because it boots on your other machine and is a factory disk. Do you get any error message? How far along the boot process do you get? If you paid for your disk, are you entitled to support? If so, contact the Freespire people and ask.
When you boot, there is a pause at a command prompt and you are able to enter boot parameters to tell the computer to bypass things that are problematic. These are called boot "cheat codes". See here (there may be some info on Freespire's site, I don't know, I don't use it): http://www.knoppix.net/wiki/Cheat_Codes
From my reading, common ones that are used are acpi=off, nodma, noapic, but you need to google for your hardware to see what's worked for others, or just try different ones and see how you go.