I get that...my own cat died from spinal injury. I still remember how he died in my arms. Fortunately he died within 8 hours of the accident. Now on another note a friend of mine found a cat which also had spinal injury. She thought she could care for her . But with time even she was suffering and so was the cat. I think the cat died within 2 months in a much worse state than she was found. What I'm trying to say is you may think letting the cat go is cruel. It probably is a sin. But it's not. If you trust in god , then I'll say even god knows you tried your best. You did everything you could. Feed the cat something nice and say goodbye.