How would I install Ubuntu on a laptop with no functional internal optical drive and that cannot boot from USB?

The laptop has a hot-swappable bay that can contain either an optical drive or a floppy drive. So I was wondering if I could boot from floppy and install either from a USB flash drive or an external USB optical drive.

Or is it possible to install Ubuntu on the hard drive from another machine? Right now I have the hard drive in an external enclosure.

Thank you.