I think Thorbjorn Ravn Andersen is probably correct. But if there's hope at all for you to reconcile with the company, it would likely have to be through the people that you worked with before and it would have to take place outside the company; you're unlikely to reconcile during an interview or application process.
Remember that although companies can be soulless and cold, they are run by people. It's people that you must have left a bad impression with the first time and it's probably those people that told HR they would prefer not to rehire. In fact, it wouldn't surprise me if there is actually a "rehire" flag on employee records at some companies.
Do you have any contact with your former co-workers or supervisors? If you do, and you're on at least neutral terms, have a lunch with them and discuss your interest. If you were a jerk in the past, it's a chance to make amends. If they were the ones who were jerks, well, then I'm not sure why you'd want to go back, but at least you could discuss things with them.
I actually did return to a company that I'd left and that's how I did it. I met with my old supervisor outside work and expressed my interest in returning.