You can try removing the memory modules to see if you hear a two beep pattern on attempted power up.  If you do not, the board is history.  
Please advise which board to post on: Dell Studio 1558: While on AC, screen suddenly went blank as if it had been unplugged. Battery is/had been functioning properly. I did unplug and re-plug a couple times, small light above power jack did not come on. Checked adapter with another computer, adapter is good. A day or so later checked again and the little light would come on. It did so several times, but then it didn't, the light will not come back on. Any easy way to check if it's the motherboard? What else could I check? Thanks in advance for any advice.
Studio 1558: Bad Motherboard?