I will add to heynnema's comment by adding that you would want to do some other hardware diagnostics as well. Really, what you want to do is rule out hardware problems as much as possible at this point. Once you determined that it isn't an issue there then you can focus on a potential software problem.
1.) Make sure your CD media is working correctly by selecting the 'Check CD for defects (very dated images on this page, but you get the idea). My recommendation would be to switch to using USB sticks. Besides being faster, you won't worry about scratching them.
2.) Check your HDD for errors with the 'Disks' utility that comes with Ubuntu. The Live-CD has it already available.
Check the 'Assessment' first, which is a simple output of the last SMART values check. You may want to run a new check by pressing the options button in the top right and selecting "Smart DATA & Self test".
This will give you an initial indication of potential trouble. But SMART data isn't always indicative of all issues. You may also have to do a surface scan of the drive.
3.) Check your memory for issues. Memory errors can creep up on working systems at any time. Choose the 'Memory Test' option on the boot selection of the Live CD to perform a memory test. This will take a couple hours (depending on the amount of RAM you have).
Once you have made sure it's not a hardware issue, you can move over to check for software/driver issues.