Paralyzed Rat

Question
I have an almost 2 year old male rat. a week ago I gave him a bath and when I put him back in his cage I noticed he was walking with a small limp. As the days go on, his limp got a little worse. Then seemed to get better. He was walking around, climbing, eatting, etc.
Then last night when I came home from work I noticed that he didn't move when I came into the room to say hello. His brother didn't want to leave his side. So I picked him up to find him completely limp. He started to grind his teeth and some black stuff came out of his mouth. So I cleaned that out of his mouth, it looked like chewed up tobacco. Which there's no way he could have gotten to, since no one smokes.
So now he won't use his entire right side, his eye doesn't close or blink, he has no feeling on his feet either. When I try to lay him on his left side he rolls over to his right.
I've had him wrapped in a towel with me since I found him and have given him some water in a dropper, which he'll take small amounts of. He seems to want to eat, but doesn't have the energy, even soft foods such as baby food or smashed and soaked canned dog food.
He's also doing some major twitching on his left side. His mouth with start to twitch really fast and that then moves down his body.
I want to give him the best life he can have, no matter how short it may be right now. So putting him down isn't an option unless he gets to the point where he looks and acts like he's in pain.

Answer
It sounds like it is neurological.  It could be a stroke or an aneurysm.  If it is either of these, he probably wont recover.

I do understand how you feel about not wanting to put him down unless he is in pain, but you must also consider his quality of life.  He doesnt have to be in pain to be suffering. Not being able to move around, eat, drink, groom himself and simply just lay there paralyzed is no way to exist, esp for a rat. Rats are proud, strong, brave in their own right.  When a rat dies in the wild, their cage mates consume their body so predators do not get it.  This is a sign of respect even if humans think its morbid. The rat, if he could talk, would tell you that they want to die with dignity, not lay there with no quality of life.  
However, only the rat owner knows for sure what his rat is capable of doing.  If you tell me that he is trying on his own to be mobile and move around propelling himself around, even if he is dragging his legs, and that he is eating readily for you when you feed him baby food and he is accepting your cuddles and will brux and boggle for you and still has the spark in his eyes that makes us love rats so much, I would say he still has quality of life and no, you should try to treat him by trying steroids for inflammation and perhaps having a CAT scan done to see if he has problems with his spine, perhaps nerve root compression that is stopping him from walking.  There are many tests the vet can do and you can make him comfortable with medications.  
Do you have a good exotic vet or is your vet just a general vet that sees rats and exotics on the side?   His conditon warrants treatment from a vet experienced in exotic medicine so if you need names please let me know.