DMV, Registration?

So I bought this 2005 Infiniti G35 Coupe like 5 to 6 months ago, and it had valid tags for a couple months from when I bought it, and the tags are expired now and I cant transfer the car into my name unless it passes DEQ, and I went to DEQ and they said that my Oxygen Sensors need replaced, so I replaced them, and I went to DEQ again and it didnt pass again, so my friend told me to register it out of city limits at like a family members house because the DMV wont make me go through DEQ, and my aunt was okay with me doing that, so she gave me her address, I called them DMV and they said she would have to be with me, the only thing I'm also concerned about is that we wrote up a bill of sale and it was a lost title, and I finally got the title, and it said I have to sign the little box at the bottom which i did, and the guy i got it from told me i have 14 days to turn it into the DMV, and I signed it the day that i went to do DEQ and it's been well past 14 days, so what will i have to do? File for another lost title? Will i just have to pay a fee? What's going to happen now? And does the bill of sale expire? I'm just confused and frustrated on how this sh** works, I just want to get the car registered in my name and have this all be done with.