Windows 7: Dell Inspiron N5030 Won't power on

I'm hoping I put this in the right thread.
Here is my issue:
I have a Dell N5030 laptop. I recently did some maintenance on it by replacing the power jack thinking that it was not recognizing the adapter for some reason. However I am still not getting any power from the adapter.

When the battery is in the Laptop the machine will start to power on, but before anything can show up on the screen it powers back down. I'm unsure of how to proceed.

Does anyone have any advice on how to troubleshoot this issue?

Sounds like the battery is discharged and can't hold power up because of that.

If you unplug the AC cord and battery, press the power button for 30 seconds to reset, then plug back in the AC cord, what happens?

Now repeat that but hold the power button while plugging back in the AC cord. Any change?

You'll need to get power into the PC to see if it will hold power up.

Thanks for replying Gregrocker.

I followed your steps. When I plugged the AC cord in nothing happened.
I held the button and plugged it in and again nothing happened.
Then I held the button and put in the battery and something DID happen.
Normally if the battery is left out for awhile I can get power to come on for about 2 seconnds. This time the power came on for a little bit longer and the Dell logo came up!
The AC cord I am using is a PA-12 Family cord. 19.5v 3.34a
P/N: 0TJ76K

I had a proffessional replace the DC Jack so I am confident the repair was done correctly. That said, could there be another MOBO issue that is not allowing power flow from the AC cord to the Laptop? When the AC cord is plugged in there are no lights to indicate a charge.
Are there alternate methods to getting power into the laptop?

Thanks again for the reply.

Did the professional you hired to replace the jack test to see if it was getting power via A/C adapter?

If not that needs to be done. I'd also have them plug in a compatible adapter to see if it works. If not they should have a power supply to plug in to see if that solves it. GeekSquad keeps theirs under the front counter for this purpose - I sometimes call to see if they're not too busy to hook it up for me.

What would I need to test that? I have tried other power cords, could that have caused the issue?
I will take it by Geeksquad if I can.

Geeksquad tested it. The adapter is fine. Still no power to the laptop however. I also know its not a RAM issue. I now believe the DC Jack is the issue still. Not sure what else to check.

What else did Geek Squat tell you?

Not much. They think its a motherboard issue. I think It would have something to do with the power Jack since I can get some power from the battery.

You would know for sure if you could borrow a charged battery for the same model. If it didn't stay booted then I would also question the mobo.

How exactly does it behave when on battery - every step.

It operates for about 5 seconds. From the time I press the power switch the front lights come on, the screen tints grey, then it powers down. Last time it powered on the dell logo showed up, then it powered down.