We can't offer much without knowing what model system (Inspiron 5521, XPS L501x, etc) you have.
If you haven't already:
Unplug the system and remove or disconnect the battery.
Hold the power button for 30 sec. Remove and reinstall the memory module(s) if they're removeable.
Try powering up on AC only (no battery). If the system will, but won't with the battery connected, the battery is faulty.
If the system still won't power up, the mainboard is bad.
My laptop is inspiron n7010 and I have tried doing the battery thing and still same results. Also I did replace my motherboard couple months ago. So, I don't know what the problem could be
Most sellers (with the exception of private ones on EBay) will provide a 90 day parts warranty - if you purchased from a seller like parts-people.com, they'll replace the board for you.