Thanks to many people here, today and in the past, I have successfully installed Ubuntu 13.04 64 bit alongside Win8. It took about 28 hours to get everything running correctly. I dug into a UEFI bios and learned many things. I downloaded Boot Repair as the final step in getting Ubuntu to be recognized. Got the ATI proprietary driver installed. Running the Torcs game with the onboard ATI gives me over 100 fps. Amazing.
I have been around the forums quite awhile: mostly reading. (You never know when you might be faced with the same problem as someone else here.) When I unpacked the new computer yesterday, I knew I was probably in for a fight getting Ubuntu installed, but thanks to all the people who have helped other here, I was pretty much prepared.
Many thanks to all those who participate here!
PS: Win8 absolutely sucks.