Cannot boot from hard drive error message

I bought Mountain Lion from the app store. I downloaded it and launched it. It began to install but when it asked what disk I wanted to install it on and I clicked my hard drive it failed with the message that I could not boot from this hard drive. So, I figured that the installer needed to be on an independent disk. So, I burned it to a DVD and ran the install program again. I got the same message. So, I plugged in an external drive, went to system preferences and set it as the startup drive. Rebooted onto the external drive. Ran the installer from the DVD and it failed at the same point. I tried selecting the external drive but it said that it was the time machine drive (which I guess was equivalent to "NO"). Anyone know how to fix this? Thank you.