DMV Registration Question Please Help.?

Can someone help me with this dilemma? The problem is I was leasing a car for 2 years. Then decided to pay it off. It was under my name and my cousin as a cosigner. So I sent them a check for 37, 600. I received the pink slip with my name and my cousins since hes a co signer I guess. And everytime I would get pulled over I would show them my insurance and registration and not have a problem. Anyway I dont know how but I lost the registration, so I go to the DMV and they tell me since you paid off the car, you need to register under your name again or some bullshit like that. So theyre telling me I have to pay 4000$? Does it make sense to charge that much for a 37k car? I baught another car 2 years ago for 25k and paid 2k for registration. The math doesnt add up. But anyway, I have to go to court to show proof of registration, what I did was buy a 5 dollar thing saying the car is registered but not completely, they told me it might go through it might not. Will I have a problem with this 5 dollar paper with the cops and court? And also I plan selling the car, will I have a problem with this registration thing? What can I do to avoid paying the 4k? It doesnt make sense at all, when I would get pulled over before I lost the registration there wasnt any problems. Why is the DMV telling me otherwise? I need help.