Dell Studio XPS 1640 won't start

I had a problem with the DC power input jack earlier. The battery had died down and the power didn't reach the motherboard. When I opened the laptop, I found that the 5 wires that connected the jack to the motherboard were broken (I mean the soldered part with the jack was broken, so the wires were detached.) I tried soldering them back, but it didn't work. However, this is what I had found after soldering the wires and putting everything back in place:
1. Without the battery, and only the charger connected - the lights on the side didn't light up.
2. With the battery charged and the charger not connected - the laptop didn't start
3. With the battery and the charger connected - the lights on the side lit up. But the laptop didn't start.

Basically, pressing the power button in all the 3 cases didn't result in anything.

So I replaced the power jack with a new one. Again, I have the same scenario. The lights on the side only light up when the charger AND the battery are connected, but nothing happens when I press the power button. I even tried pressing the power button for a long time to release the static charge build-up, but nothing happened. Now I feel that I had soldered the wires correctly, but there is some internal problem. Wondering what it could be. I am pretty sure I haven't messed up with any other connection inside the motherboard to make it go crazy.

 

If you replaced the power jack and it's still not working, the motherboard is most probably bad. Something probably died and shorted, which may explain why the solder joints on the DC jack melted/burnt off.

 

What is the best way to rectify it?

 

I mean, you'll have to buy a new motherboard. They're probably around $100, so it may be more worthwhile to just get a new laptop.