Go into the BIOS setup (F2 at powerup).  Does the system recognize the AC adapter? 

No:  the battery won't charge.  Try a new Dell OEM adapter.  If that doesn't solve the problem, you either need a new DC jack or a mainboard repair or replacement;  the jack is part of the mainboard (not separately replaceable without soldering).

Yes:  is the battery OEM, or third party?

If OEM, return to Dell for replacement.  If third party, contact the seller/manufacturer.

The problem is the battery indicator shows Blue, but the laptop shuts down after 1 min even when it is in BIOS.

I managed to see in the First tab of BIOS, and it reflected something like '90W adapter'.

I guess it is detecting the AC adapter.

I take the battery out and try to turn on the laptop, but it cannot start at all.

BIOS version I am on is A06.

I don't know if I can upgrade the BIOS, when the laptop keeps shutting down.

It is a third party battery, I have already contacted them, and they have suggested to set the 

POWER-->Start Battery Calibration, and then update the battery to "known".

Can anyone please tell me if this(highlighted in black) is achievable, considering my laptop's condition right now?

You absolutely MUST NOT try to update the BIOS on any system that's powering off at random --  that 's an invitation to a dead system.

If you've never cleaned the heatsink assembly of dust, start there -- overheating can easily cause shutdowns. 

If the notebook won't turn on with AC only -- and the AC adapter LED is on -- there's something wrong with the mainboard.

I've cleaned the heatsink assembly of dust, but the problem still remains.

I've observed another thing with my laptop.

Whenever I try to enter BIOS, it says, 'Battery Not Detected'.

I assume, it needs update on BIOS, because I saw the same behavior with another battery as well.

The laptop is simply not turning on directly from AC adapter, if I remove the battery and try to turn the laptop on.

At this point I'd suggest replacing the system board.

So what is the solution?

I just worked on my laptop to see what exactly is wrong with it.

1) I asked my friend to see if the adapter was a problem.

2) I plugged in my new battery into his Dell Vostro 1510, where it was detected. His charger started charging the battery successfully.

3) Once the battery was charged, I plugged the battery again into my laptop, where the laptop did successfully start.

4) I plugged in his AC adpater (PA10 65W OEM) in my laptop, and also the battery, where I found Windows showing me "Plugged in, Charging". 

5) But I noticed the battery wasn't exactly getting charged in my laptop, whereas the windows showed me a contradictory situation. The battery showed me it gradually was decreasing, even when the AC Adapter was plugged in (The front LED indicated Blue, meaning it was charging the battery).

I really don't want to make a decision on Motherboard first, but want to really know if this situation can be fixed somehow.

BTW, I did manage to upgrade BIOS on my laptop when the battery was at considerable level. But that hasn't even helped to Charge the battery, even when Windows says 'Plugged in, Charging'.

Any pointers, what can I do next?

There are two different boards, depending in whether you have Intel or nVidia video

http://www.parts-people.com/index.php?action=category&id=145&subid=267&refine=motherboard

Hi,

Can anyone please help me here?

On the weekend, I called a person to see if the power jack was a problem, which didn't turn out to be.

The motherboard is working fine, (I can confirm this by plugging in a charged battery, and it runs on the battery as well).

What the person said, the part which transfers over the power from the power jack onto the motherboard has gone wrong.

Can this be fixed?

If not, I am OK to buy a new motherboard. But don't know the Dell P/N for it. How do I know the actual P/N for my motherboard?

Also, I checked the Dell website if I could order a new one (or Dell refurbished one), but didn't find any.

Can anyone please tell me where I can find the relevant information?

Mine is definitely not Nvidia graphics one.

Will it matter if I use the Nvidia one, instead of one of the other two?

Also, from the other two which one do I choose?

VGX00 OR U654J?

Again, is there any way I can get it within United Kingdom?

The seller is based in US.

And if there is any Dell service here itself where I can get it replaced/repaired?

Can anyone please help?

Any 1520 UMA (integrated video) board will work as a replacement.  For UK suppliers, try a google search.