First, you need to get food into him ASAP. He's been way too long without. Warm him up, rub his little body with a warm towel to get him stimulated. Then you need to start hand feeding.
1 can goats milk
1 can water
1 teaspoon baby rice cereal
Mix it up and give it to him at room temperature. I use a syringe, but if you can't get ahold of one, get a glass eye dropper. Place a drop of the formula on his lip at a time, and let him lick it in. Consider yourself lucky if you get a few drops in the first time. Wait a little bit, try it again. After that, if you get him eating, you need to take care of his bodily functions. Gently rub his genitals from front to back, down over the rectum, with a BARELY moistened warm cotton ball. You don't want to soak him, you want to stimulate him.
You're going to need to hand feed him every 2 hours around the clock, and take care of defecation and urination. Set your alarm clock. If mom is absolutely not paying attention to him, then put him in a carrier with a heating pad under half of it on the lowest setting. Give him a stuffie to cuddle with as well. Every time you take him out to feed him, try placing him back in with mom again and see if she takes him. Make sure you use mom's shavings to put in the carrier where you are keeping him.
I would not put him in with mom, and then just go to bed, even if you "think" she's accepting him. Do it while you know you can keep an eye so you can pull him if need be, feed him, and warm him.
Once you get him eating and moving again, mom may take over. With him being so cold, she may be rejecting him because she thinks he isn't going to make it.
Also, GENTLY move his back legs up and down in as natural a motion as you can. Slowly and gently. Continue to rub him with a warm towel from head to tail trying to restore circulation.
After you get all that going, read through the FAQ under the breeding and baby section about caring for kits. That should give you all the information you need in more detail.
Good luck!
ETA: If he got out of his cage, is it a baby safe cage? If it's not, you need to either buy a new cage, or somehow turn this into a baby safe cage so it doesn't happen again.