You sound like you are describing a ram issue. The ram is by far the most likely cause of any kernel panic that your computer experiences. I would remove all the ram sticks in your computer. This guide will show you how to remove an reinsert ram into your computer:
After you remove all the ram, reinsert 1 stick into slot 1 and boot up. If there is a kernel panic, then reinsert a different stick and try again. This will show you what ram sticks are bad (kernel panic) and which ones are good (boot up). If you get a kernel panic on every trie then you most likely have a different problem. You ram might also need to be removed and reinserted. You cannot use a ram stick it it is bad. You may even want to buy new set from OWC to replace the aging set that you currently have installed. If this is not the case, then you may also want to try the hard drive. Hard drive caused kernel panics are far less likely but are still a possibility for any mac. Tell use what you find so I can provide any further assistance if needed.
Hope this helps.