I HAVE A PSP 1002 (ORIGINAL MODEL). the problem is that i tried charging the battery with the wrong charger (i had temporary lost the proper psp charger) this seemed to work for a little while until one day the battery died. I tried charging it again with the proper psp charger but it will not charge anymore. I have bought replacement battery which worked until the charge ran out and then it will not recharge. I have tested my psp charger and battery and they work. the problem is the psp will not charge the battery.(the red charging light does not turn on either)

Unless you have enabled the actual USB charge settings on the PSP you probably won't be able to charge it via a USB cable.
The simplest solution here is to buy a replacement mains charger. They are usually reasonably cheap to buy for a decent quality one. I personally would avoid the really cheap ones as they are not always as good a quality as an original Sony charger.
Another option is to buy a Docking Station for the PSP. Some of these are a table top stand that plugs into the mains electric supply. You then sit the PSP into it, attach a short power wire from the stand and leave it to charge as normal. There are other versions where you have to remove the battery from the PSP to charge it.
The batteries are actually quite easy to remove and replace so you could consider buying a spare battery as well as a backup.

cheak that the bettery is out of order if this is not than change the jak of charging

Have you tried to remove the battery and put it back in and try to turn it on. Try removing the battery and putting the charger in and starting the PSP. If it starts, it might be the battery. If it doesn't, it's either the plugin for the charger or the PSP is just dead. If it does start with the charger, try putting the battery back in, if it charges awesome. If it doesn't the battery might be dead.

Theres several possibilities on what happened. if you dropped it recently or something like that, you probably broke it; open it up or send it back if still under warranty. If its really old, then the battery may have lost its ability to retain a charge. Also, your charger may not be working properly.

Solution 1: Try to borrow from your friend psp charger and charge it if charging. this maybe the problem.

Solution 2. Try to borrow replace the battery if it will charge. This may be the problem.

Otherwise the problem would be the psp unit itself that you are using while at battery charging. Hence your are playing and moving, you have tendency to damage the charging port of your psp. This maybe the problem and need replacement of parts.

The battery is done. To run it, just remove the battery, and run it off of the charger. That's what I did until I got a new battery.

the usb for the psp is only for tranfering data not for charging you still have to plug the original power supply charger in when your psp is connected to your pc

this is simple, there are only two things tht can be wrong or faulty:
1. your charger is messed up, or it simple is not an original dell charger in wich case replacing the thing with an original D600 charger will fix it.

2. your battery is messed up and u may need a new one or its not an original

Mind you many parts of a dell are configured only to worked with same model and original pieces so make sure all the parts are real then if the problem persists, check (for the charger) when the wire is wriggled wether the little green light flickers if it does replace the charger if not try the laptop with somone elses battery to see if it works well if it does change batteries if not then its an internal wiring problem and the warranty will cover tht altough it is Highly unlikely that wiring problems will be present...

The way to properly break in a lithium Ion battery is to run it dead before you recharge it. Then fully recharge it and run it until it's dead again. Do this about 3-5 times and then the battery is properly broken in. If you charge it before it dies on a new battery you can build what they call a "memory" where the battery thinks it's fully charged however it's only maybe half charged and you will lose alot of life out of your battery. So make sure you properly break it in.

The polarity of the charger you used is wrong or the wrong voltage, and has messed up the programming n the battery.  You may be lucky if you get a new battery and use the Right charger, It might fix it.  Sony put a battery in the PSP that has a memory chip in it, and I think it will automatically disconnect if the wrong vooltage hits it, or wrong polarity. be warned that I have seen where someone got a new battery and it did not solve the problem. If this happens to you Contact Sony at the following number.

SCEA Consumer Services
1-800-345-SONY (7669)
Monday - Saturday 6:00 AM - 8:00 PM PST
Sunday 7:00 - AM 6:30 PM PST