PSP Won't Turn on or Charge

[!!??]

I bought a broken PSP slim off a friend for a cheap price. The problem was the screen(it wasn't plugged in but cracked anyway). So I took it apart found out the screen was cracked, and after turning it on(while it was apart to check the screen) the psp shut off. Anyway I try it again thinking I might have blown a fuse and it worked fine. So anyway I put it back together turn it on to see if it is working, again, it turns on(you hear it start up and hear the xmb the backlight turns on) and then it turns off by itself after a minute. Then I turn it on again it starts up and then it shuts off again but after about 30seconds. Then again about 10seconds, then again 2seconds, then it would turn on but instantly shut off, and finally it wouldn't turn on again at all. Me not having much experience with playing PSP's just figured the battery(which is a new non oem one btw) ran out of power. So I try charging it with a new Ac adapter but no light comes on and it doesn't charge. I tried turning it on with the ac adapter without the battery in and the same. Now I have a PSP lcd that I want to install, but the PSP won't turn on. Should I just sell it on ebay, and buy another one with a broken LCD? or is it an easy fix?

[Buddy4point0]

Well if you sell it on ebay, you wouldn't make much. I don't know how many people would buy "PSP, doesn't turn on."

It doesn't sound like a broken LCD.
I've broken quite a few and I've never had this problem.

So I don't know what to tell you.

[!!??]

Well if you sell it on ebay, you wouldn't make much. I don't know how many people would buy "PSP, doesn't turn on."

It doesn't sound like a broken LCD.
I've broken quite a few and I've never had this problem.

So I don't know what to tell you.

The thing is that the PSP would turn on(no screen but you could hear it start up). I opened it up found out the lcd wasn't connected. I turned it on and the lcd was broken(the backlight turns on but it looked cracked other than that). After putting it back together it would turn on but turn off after a certain amount of time that decreased with the number of times I turned it on until eventually it wouldn't turn on at all. I already have an LCD replacement thinking that it was just the battery running out of power(didn't check to charge it until a few days later). It doesn't charge at all either.