As far as I'm aware; once you start booting from a Linux live CD, whatever OS is on the HD is completely ignored. So the resident OS will not be able to stop the machine booting from the CD (The BIOS settings usually determine whether boot from CD/DVD is allowed!). Similarly, once running a live distro, the resident OS shouldn't be able to stop the HD from being reformatted either.
If your Linux live CD's are failing to boot, it is most likely a hardware related issue (or your live CD is scratched/damaged/corrupt!). But it's not necessarily the HD, it could be something else, like a component on the motherboard or some other card/component which is damaged.
What happens if you remove the HD's and then try to boot into a Linux liveCD?
If it boots OK, then the HD's are definitely damaged. Otherwise if it doesn't, then there is some other hardware related issue!
One other thought springs to mind:
256Mb of RAM doesn't sound like enough to be able to run Ubuntu in Live mode (but I could be wrong), perhaps you could try a more lightweight Linux LiveCD. Perhaps something like Slitaz (which is Ubuntu based, but far more lightweight).
Try booting a lightweight distro's live CD without the HD's connected first and then if that works, try booting with the HD's connected.
If Slitaz (or whatever lightweight distro you choose to test drive) boots OK both times (with and without the HD), then you should be able to format the drives and install a distro on there.
If Ubuntu is your preferred distro, you could try installing Ubuntu using the alternate install disk rather than the liveCD. The Ubuntu alternate install disk requires much less memory than the LiveCD, so is more likely to succeed on a system with less RAM.
However, if even a lightweight distro won't boot without the HD's connected, then you'll know you've definitely got a hardware problem. In which case, something like the Ultimate Boot CD might also be of use. The UBCD has tons of diagnostic tools that could help to determine the exact problem (provided the computer is able to boot into UBCD that is!).
Oh and purely for the purpose of reformatting the HD's, you could perhaps try removing them, connecting them to another computer and then reformatting them from there.
Again, if this presents a problem it is most likely that the HD's are dead/damaged!