Battery not charging and/or laptop shuts off though battery shows more than 50% charge

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this first began last month while using my laptop - it said low battery and shut down.  I plugged in the charger and restarted the computer.  I checked the battery status and it said it had 52% but was charging however 10 minutes the laptop shut down again, despite being plugged in. I turned it back on and checked battery which then said it was not charging but still had 50% power.  I took my laptop to Staples to get a new battery but the tech there said battery was fine, I needed a new charging adaptor.  I purchased a new charger and experienced the same problem with the new charger.  I returned the charger and explained to the tech it didn't solve the issue.  I have ordered a new battery but have noticed that the port to connect the charger is loose (both old and new charger had same loose connection).  Is this an indication that the plug in port is damaged?  Is this easy / affordable to replace if this is the issue?  This laptop was purchased just 2 years ago.  

[Huffer · Accepted solution]

Here is the Service Manual:

Manual

So did you replace the battery and the AC adapter and still have the same problem or did the tech talk you out of a new battery?

He or she should have made no such suggestions without running a diagnostic, which is built into the software and BIOS on the laptop. 

There is naturally some "play" where the adapter plugs in but if its sloppy it is very possible the charging port cable is bad.

It is a separate part not soldered to the motherboard so can be replaced without tremendous difficulty or expense but does require some significant disassembly..

One way to do a quick and dirty test is to pull the battery and see how it runs on AC adapter alone. If it fires up and runs OK on just the AC adapter, then it's likely not the power jack that is the problem.  From the Manual I see the battery is the clip in kind not the kind you have to open the case to replace. 

Answer my questions here and we can figure out what you need to do.