Whether you can register the car or not, is not your biggest hurdle here. Because somebody else (a finance company or bank in this case) has a financial interest in the vehicle, the law in Queensland states that the car may be repossessed by that finance company or bank as a means of recovering the debt, even though the debt was not incurred by you.
Fundamentally, the private seller who sold you the car was not legally in a position to do so for the simple reason that the car was not theirs to sell. Because that financial institution still had a stake in it (as loan security or whatever) the car was not fully owned by the private seller. The car did not, as the law calls it, have a clear title.
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If the financial body decides to repossess the car, you would have the choice of letting them do so (and waving goodbye to your money and your car) or paying out the amount of money in dispute. Either that or contact the seller and convincing them to make good on their loan repayments.
You can avoid this situation by doing a PPSR check (in most states) which will alert you to a vehicle that is encumbered. The official advice it to never buy a car with money still owing on it or is in any way encumbered. The other alternative is to buy from a licensed car dealer or trader as, under the law, they must guarantee clear title on any vehicle they sell.
So, before attempting to spend more money on registering the car, talk to the company with the interest in the car and try to come to an arrangement regarding the car’s future. You will have very little recourse if the car is repossessed as the company involved is well within the law to take this action.