Can you install Ubuntu directly to a HDD?
Solution 1:
I am not quite sure what is your problem. Can you boot using a live CD at all? If yes, you will discover you have the option to install Ubuntu on your hard disk from the live CD. If you have problems with the live CD and assuming your computer is new enough to boot from a USB stick, you can "burn" the CD image on a USB stick using a program like http://unetbootin.sourceforge.net/
In general, if you decide that Ubuntu is your OS choice, you should install it on the HDD. It will run much faster, not to mention that you will have much more freedom.
Solution 2:
If I understand correctly, you are looking for other options beyond liveCD and bootable USB (somehow putting the ISO on your hard drive, booting it and installing to spare space from there sounds quite tricky, starting with the fact that you don't want to use your CD drive or USB).
Some alternatives are 1) A netboot install 1, if your PC can network boot or has a functional floppy drive. 2) transplanting the hard drive to a PC with functional CD drive or USB for the install, before moving it back again - this would require some work tweaking GRUB, most likely.
Hope this helps.
Solution 3:
I had a similar problem and came up with this solution,
Connect the hard drive to a normal windows/Ubuntu machine via a USB-IDE adapter, run Unetbootin and use it to create a bootable drive on the USB mounted hard drive.
Put the hard drive back into the old machine with no USB/CDrom drive.
Works like a charm :-)