I'm sorry to hear about your challenges.
Before I answer your question, I think it would be helpful to explain why some companies run credit checks on prospective employees. The logic is that if a person can’t handle their financial affairs, then they probably can’t make sound decisions for a company, nor can they be trusted with making decisions within a company that involve handling company funds or making important financial decisions for the company.
Another reason for checking your credit is to see if the salary they’re potentially offering you is going to be sufficient to cover your expenses. During recessionary times such as now many desperate people will take ANY job they can get in order to stop the flow of money out and to keep their heads above water. However as soon as they get a better offer, they’re out the door! A potential employer wants to see that you’re there for the “long haul.”
I'm going to answer your question based on the assumption that you lost out on the job because of your bad credit. A 2003 study that was done by the Consumer Federation and National Credit Reporting found serious errors in more than a third of consumer credit reports. So even IF your credit was stellar, there's a one in three chance that your credit report is going to have errors on it that will adversely affect you. That alone gives you a fighting chance to reframe your credit.
Remember that your credit just shows amounts, dates, lenders and such. It DOESN'T give a reason WHY. And that is the Ace in your sleeve.
Who's to say that you weren't a victim of identity theft? With the explosion of identity theft many people are living in a Kafkaesque nightmare as they try to turn their life right side up.
Perhaps you had a family relative that was suffering from a terminal illness and you did what you could to help them financially during their last months, but in the process got yourself in a financial jam and now your credit is messed up.
If you can, go back to your potential employer and ask them where you are in the hiring process AND mention one of the suggestions above and see if that gets you back in the door.
Generally speaking, if you know upfront that your credit is going to be run, take the initiative and reframe the story to YOUR advantage. By mentioning your bad credit BEFORE they pull your credit you get a chance to defuse the situation.
Let me know what happens. Good luck!