How to fix my dead PSP-2004?

After a long time. I was not using my PSP for a long time because my memory stick broke. I tried to check it out. I charged it and changed my settings. I switched it off, after a while I Turned it back on but it won't. I removed the battery and plugged my charger and bam! turns off. I was relieved but when i removed the ac adaptor it turns off. Please help is it broken?

Or what?