It could be the battery itself is bad or it could be a fault in the power supply module or the charging circuit. its very awkward to tell without viewing the machine.

you've already ruled out the probability of it being the AC power cables however it seems a bit peculiar that on both of them the green light on the box goes off.

May be best to ring Dell support for further advice and see if they can come up with any further ideas. Dell are specific with their parts unfortunately.

Hello,

My name is Mike, I’m a Dell Technical Analyst located at Dell corporate headquarters in Round Rock, TX. I'm part of an internet outreach team developed to interact with the online community regarding technical questions and issues that customers face with Dell products. In reading your post and the steps you’ve taken to resolve it there are a couple of steps to consider. First, I’m sure the adapter that your mother-in-law gave you was a Dell adapter, looking up the specs for the system online at www.support.dell.com and clicking on the “User Manuals” link you can check to make sure that it is the proper wattage for that system. You may also want to check the power rating on the other adapters you used. If the system uses more power then the bricks you are using it may explain why the LED goes out when they are plugged in. Second, with what you’ve described it may also be experiencing a grounding issue caused either by a damaged or loose charging board as mentioned by JANINE, or it may be as simple as a screw missing off of the chassis. If you have any questions or comments please feel free to email me at customer_advocate@dell.com with my name in the subject line: ATTN: Mike B., and I’ll get back to you ASAP.

Thanks,

Mike.
Dell customer advocate

[Quote=janine]Second, with what you’ve described it may also be experiencing a grounding issue caused either by a damaged or loose charging board as mentioned by JANINE [quote]

It seems like you may be agreeing with me here Mike. Thankyou it gives a Trainee MCSA a great sense of achievement.