Iphone keeps trying to turn on but won't?

I have an Iphone 3 gs my dad gave me a few months ago, it's 3 yrs old so pretty old. It was working perfectly fine when i got it except the vibrate button was messed up, when i put it on vibrate it kept going on then off. I did drop it a coupe times and cracked the screen and then after using it for a while( i was on it constantly) it started to not charge right. It got to the point where it wouldn't charge on the wall charger, car charger or computer, or on different charge cables.

I finally got a little bit of money and got a new screen and new battery. The screen looks great and the battery worked great but was only at 30 something %, which i know is typical for shipping. But when i went to charge it (at 12%) it wouldn't get anymore charge, it just stayed at 12%. I left it plugged in all night hoping it would do something but didn't. I took it off the charge the next morning and went to plug it back in and it wouldn't charge or indicate it was charging where as before it indicated it was charging by the charge symbol but the % wouldn't go up.

so now when i plug t in anywhere it has the apple symbol like it is coming on for a few seconds (maybe 2-3) then it'll go away then repeat the process, it won't get off the apple screen, i would just reset it but while putting the screen back on i super glued the home button down (it wasn't working good before anyways) so can't reset it and iTunes won't recognize my phone when i plug it into the computer.i'm real computer savvy and know a lot about electronics but just can't figure this out

Your iphone is bricked… Check out the tutorials for resetting without a home button.

Had the same issues with my iphone 3. Took it to Apple Store and they determind that there was a short between where you put the charger in at and where the phone sends the charge to the rest of the phone. Replaced my entire phone