Chick had a hard time hatching and now is weak

Ugh...
we had a hard time this round...
had a power outtage and I think it messed up my bator, so not only did it get down to 88 in there once until the power came back on, but then it shot up a few times to 115!!!
I figured they were all dead... but amazingly we had two hatch out!
then, a third started out, and by morning, a fourth was out!
the third however didn't finish hatching...
he peeped a lot... and got a hole the size of a nickle, but didn't go 'around'...
so eventually I helped him just a bit...
then a day later a bit more...
and my daughter realized he was drying out in there and peeled the rest of one half of the shell off, but he still couldn't get out...
I took the rest of the shell of night before last, and cleaned him up some, but he couldn't stand... but peeps LOUD... so I put him on a wet paper towel and put him back in the bator alone... the other eggs (duds) in there too.
He didn't die!
so, now what do I do?????
last night I gave him a bath, as he was coated in 'white' from the egg and his feathers didnt' fluff, and he had a 'chunk' of white on his head.
I was dipping his beak a few times, then decided to mix some chick starter with water and syringe a few drops in to him... which went well,
I keep assuming I'll find him dead the next time, but he keeps getting better!
help!!!

this morning he stands up more, and almost walks!
not eating that we can tell tho, so we syringed a few more drops this am...
he is loud!!!
he wants to live!!! (and I sure hope 'he' is really a 'she'!)

 

s/he is still not eating....
what do you do to keep a chick alive?
help!!!
she doesn't seem to know to peck at food, or how to drink water...
ugh, maybe I just don't see her doing it?
she is making poo, but it's mostly clear, with a teeny speck of brown in the center.
oh, and she is happy, can walk now, and step up on the sponge she lives with in the bator...
I'm afraid to put her in the brooder, she is half the size of the other three... I think they'd peck her!
how am I supposed to feed her?
how often? how much? and of what?
thanks in advance...

 

OK, thanks!
I will get the vitamins and try that... and try the brooder for her tonight...
(keeping a close eye of course), maybe the others will like her?
she doesn't peck at ANYTHING, but will swallow if the drop goes in her mouth...
I have been putting a small water dish in with her and some wet chick starter in there too, as she has to go all day while I'm at work, then all night after we go to bed...

 

SHE ATE!!!
I'm SOOOOOOOOOOO happy!!!
I might even get up the nerve to put her in the brooder with the others tonight! LOL!!!
I luv you guys!