I have an old MacBook 1,1 here and want to install Ubuntu on it. However the disk reader is broken. This leaves me with a bootable USB, however this is not recognized when I boot with EFI (if that makes sense). Is there any way that I can install Ubuntu without a CD or USB drive?
Yes you can. You can use unetbootin
You can read the section "Hard Disk Install Mode" to see how you can do it here