Laptop will not stay on. How can I fix this?

Okay my laptop will not stay on for more then a minute. It DOES say that the battery may need to be replaced because it's low. Well I took the battery out and just plugged the power cord in to the wall. I still get the same problem it will not stay on. If I let it sit for a little while then go turn it on it will stay on for a little longer maybe 3 minutes. Please help.

Ok so I just tried to see if it could be overheating because it will shut down when that happens. I put a fan pointed at the bottom of my laptop and it seems to stay on. But before it did not seem like it was getting that hot. Also my battery is still out of it currently. So what should I do.
 
If it is an older laptop it is probably the power supply unit or PSU connector. Try wedging something, maybe a lighter, underneath where the AC plug goes into the laptop (or put pressure upwards with your hand). See if it a bad connection, you will be able to tell as your computer battery will begin to charge. Just a suggestion as this has happened to me and many others over the years.
 
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