Bad credit..need a place to live

My boyfriend has poor credit due to recieving a credit card while in the army many years ago (teenager) and he racked up an impossible debt. I recently racked up bit of a debt due to a credit card i used to pay off some bills when we got behind.

I want to pay the credit card bill i just CANT right now. We are trying to move and find a place to live but so far NOBODY will accept us and its getting to the point where i dont want to even apply since it costs at least 40 dollars non refundable just to get denied. What do i do?? Any suggestions?