Please pay your rent first!
is there any merit in trading in your car in its current state for something else? eg using it as a deposit against another car, or selling it on in its current condition to get a small deposit together?
I had this same dilemma a few years ago: I needed a car to work and earn money, no public transport options but had an old car which gradually turned into a money haemorrhage, I realised I would end up paying out much more than it was worth to keep it on the road, and never get any money together as a buffer or to buy a new car because of its maintenance costs
Eventually I traded it in as the deposit against a small car, on a lease scheme from a dealer, it was a 3 year deal with a service plan: and although it seemed foolish and counterintuitive to add to my up front monthly costs it made more sense in the long term
it gave me a predictable outlay each month on the cars cost with no surprises, and I knew I had reliable transport for work and everything else. As it was a small new car it was also only a £20 road tax and much more fuel efficient so I ended up saving that way too.
The lease scheme only lasted 3 years but by that stage I was in a better position having been able to work reliably and put in extra hours and shifts as I always had transport, and I had built up a bit of savings by then: I had also spent 3 years pretty stress free about transport and driving a newish, safe, well maintained car.
I could have bought the car outright at the end of the lease but at the time it was more appropriate to give the little car back to the dealer and use my savings to buy a different one that was more suitable for our needs eg childrens seats etc
It felt really scary signing up to a set monthly cost when I had been hand to mouth for so long, but in the long term was one of the best things I did to sort out my financial, transport and work stresses at the time.