there is a procedure used for verifying the integrity of the download. hash verification. most of the time (but not always) they give the md5 or sha256 at the ubuntu website. using the command line terminal in linux you can 'examine' your downloaded iso to see if it's corrupt. you can use a tool called 'hashcalc' if you're using windows.
it sounds to me like you have a good disk because you get to the screen where you choose to install, run memtest, or try ubuntu. when hardy heron came out, i could install it on every computer i own and they all booted every time and worked very reliably. something happened by the time karmic koala came out, because most of my computers at THAT time (running karmic koala) had display problems (i would install and reboot and got a black screen) and i got away from ubuntu and used other distros. I found a peculiar work around (by accident) where i used my sisters computer to install ubuntu lucid lynx on several hard drives and used them hard drives in my other computers and they worked reliably. otherwise i would get a black screen after installation and reboot. it would seem to suggest that the hardware detection was not working properly, but that is merely speculation by me. i'm just a user. I verify the hash every time i burn a disk, so it's not the disks (or the software on the disk) fault.
i have a stack of over 100 distros and i think that each computer i have has about a 50% chance of installing any given distro. you might want to consider trying another distro. fedora is a red hat derivative. and opensuse is an independent linux. just a suggestion.
