Please check if there is any light on the brick of the AC Adapter. You may try charging the system with another good known AC Adapter. Try to power on the system just on the battery and just on AC Adapter.
Keep me posted with the results. I will be glad to assist further.
Thanks & RegardsAmogh G#iworkfordellTo know more about Dell Product Support, Drivers & Downloads, Order & Dispatch status -> choose your region USA; India. For helpful Dell Support Videos, you may click Here.
Try reseating the memory module(s) first (remove the battery and power adapter before doing this)
If you can turn on the laptop with one of the batteries you have available it is possible that the daughterboard(take a close look at power jack) is faulty or just try reseatig the cable that connects it to the mainboard.
If nothing helps try disconnecting/reseating the display ribbon cable(be careful-don't break the connector),touchpad,keyboard - one at a time and check if the system reacts differently.
If you want or have to dismantle the laptop there are some good videos on YouTube
It seems the issue is with the system motherboard and it is needed to be replaced.
If you are residing in US, you may contact Dell Out of Warranty Repairs (OWR) department at 1- 800-288-4410 to check the time and cost involved for repairs.
If you are comfortable in replacing the system board on your own, you may contact Dell spares at 1-800-372-3355. For Owner’s Manual, please refer to the link: http://bit.ly/QumKWn.
Hope this helps. Please feel free to reply for any further assistance.