DiskXX: I/O error messages that show when booting in verbose mode do correspond to failed hard drives the majority of the time. It IS possible that either the hard drive cable or logic board is faulty but given the age of the hard drive it is much more likely to be the culprit. Either way the Disk02: I/O error messages are a clear indicator of a hardware issue that cannot be solved by software fixes.
If you have never formatted your disk or reimaged it with a new OS then you probably still have Apple Hardware Test (AHT) built in, which may help in giving you a more definitive answer. Hold down D when you boot your Mac and keep holding it down (can sometimes take 45 seconds or longer) until you see an icon that resembles a classic Mac with a chip in front of it. If this logo appears then you have AHT installed and you can run a quick test by clicking Test or an extended test by checking the box next to "Perform extended testing" and then clicking Test. Depending on the results you might see "No trouble found" which means all of the components passed testing or something more cryptic, along the lines of 4SNS/1/1/40000.... These codes tell you what component failed. If the hard drive is failing then I would expect to see a 4HDD error code.
If AHT isn't available then if I were you, based on the Disk02: I/O error, I would start by replacing the hard drive since the age and errors seen so far strongly point to that as the problem.
Hope that helps!