PCG-V505DC2 Charging Problem

Hello.

I have a 3.5year old Sony Vaio PCG-681L (PCG-V505DC2) laptop that I bought used from a friend a few months ago. From the last few weeks or so, I am facing a peculiar problem. The battery loses charge *significantly* even when the charger is plugged in. The only way to charge it is to shut it down completely and leave it charging overnight. This too, is highly erratic and unreliable. Sometimes it happens that I find it did not charge at all at night. Also, during regular use (when plugged in) the taskbar battery information icon sometimes toggles very rapidly between the 'charging' icon and the 'battery' icon, and then returns to the 'charging' icon. This toggling happens erratically, sometimes as frequently as 30s to a few hours in between successive 'toggles'.

For troubleshooting, I tried removing the battery (maybe it has outlived its useful life) and just trying to make it run using the charger. The laptop would invariably start and shut down within 0.5-10 seconds.

What could be wrong here? A defective battery? A (gulp) dying motherboard? I don't have a lot of cash (that is why I bought the laptop used anyway), is this a simple enough problem that I can fix myself?

 

This problem seems to be attributed to that toggling. The connector for the adapter is probably not getting the charge to the notebook, possibly because of a damaged connector on the notebook. Can you check and make sure that the connection between the connector and notebook is secure?

 

It moves/wobbles a little (2-5mm?). But there seems to be no relationship between the occurrence of this 'toggling' and me trying to 'move' the connector socket.

EDIT: Also, wow... the charging indicator is jumping around. A half hour ago it was 66%,now it is 89%.

 

Anyone? Is this something I can get fixed on the cheap?