Well, that’s annoying. If I consider the constraints you’ve listed as hard-and-fast, I think my first take would be to remove the hard drive with the current boot image to a second PC, and to install the installation boot image of the linux variant I wanted onto that disk in place of the current boot image.
Then I’d pray that the installation boot image had support for my SCSI cdrom, and wouldn’t somehow be troubled by the fact that it had been booted from an unusual device.
And although this might work, I’d still be tempted to run out to the nearest Staples and buy a cheap IDE cdrom to avoid any problems that might crop up.