My PC (dual booting Windows) lost power while I was updating Ubuntu. Now, when I start the computer and enter Ubuntu, I get a blank screen with a blinking cursor. How can I fix the botched install?
Fresh install could be the only fix. It's hard to know what it could have been writing, at the time the power was lost.
You should boot into it with a live disk first, and see if you can access anything in terms of media, or important files you'd want to back up externally.
I had faced the same problem...
One of the ways out is a fresh 12.04 install from a live cd/usb...
When you start the livecd / usb you should see an option that says "Upgrade Ubuntu X.XX to 12.04". This option will upgrade the system and leave your data intact.
This did not personally work for me, but you may have better luck with this method. Remember to try and make a backup from another operating system or a live system before you do this.