Please help, iphone doesn't boot correctly !

OK so i am going to explain step by stem what happened:

1- i was playing a game on the ITOUCH 1G and ran out of battery 0%
2- o% meanin the game went straight to the springboard and from springboard it turned off by itself
3-i plugged it into the wall to charge
4-when i press the reboot key the apple logo appears
5-only for 20-30 seconds
6- after the 20 seconds it doesnt go STRAIGHT BACK TO BLACK it goes fuzzy half a second and then turns off probobly because there's not enough battery
7-it does that whatever the manoeuver
8-i can restore it if i like but i have more than 100 apps and 467 musics on it and so forget about it


Question:
Does my itouch CHARGE WHILE it is 100% turned off

How do i get it to boot correctly without having to go throught the restore things !
I know of the DFU and manualt way by pressing home and then plugging blablabla
that works fine but is there another way of making it boot correctly


IS the solution to let it charge in the wall even thought its totally shut down ??? i repeat ITOUCH 1G

edit; i counted how long the apple logo stays; 25 seconds then turns right back off !

 

thank you i really hope it does, my dad would kill me man, like no joke, i'm 17 and if i broke it LOOOOL i won't go there !

ok how long do you think i should let it plugged in the wall ? Also, even though it's plugged in, you do realise nothing is telling me it's charging right ?


like i'm desperate right now ! I was playing taptap and i am sure as hell not restoring my itouch !!! lol thanks alot though i'm taking any advice !!!!

EDIT: It has been plugged in the wall for at least a half hour and still doesnt turn on !