Hmmm the Dell inspiron 5150, one legendary laptop with umpteen issues, a laptop designed to break.
A promising contender for the stupidest laptop dell has ever built contest. However if my laptop survives this summer it may see its fifth birthday in november.
Follow at your own risk
When you press the power button, If your laptop powers on, the lcd panel is pitch black blank screen, not even back light power, no dell startup screen, you hear the fan spin up, you hear the hard disk spin up, in this state one of the 3 LED lights blinks for 7 seconds (I think numeric keypad), and then if everything switches off silent. The only LED on after that would perhaps be the battery charging indicator. it could be a memory DIMM gone bad, If you have two dimms try one, then the other to confirm.
If you can charge your battery elsewhere and power up your laptop
it means
a) AC/DC jack on motherboard has gotten loose, use solder to fix in place, shaking the adapter sometimes shows the loose connections.
Connector related problems, The USB and the DC jack connectors frequently loosen from motherboard. solder breaks. Do not move the laptop around too much. particularly with wires sticking in from the back. the tug of the cables cause them to loosen.
b) The Schmidt trigger chip near the DC jack has come loose.
Sometimes applying torsional force on laptop and pressing the laptop it near the power button makes contact temporarily, and laptop can get power, the mild bending of the motherboard aids contact, be careful .
c) your DC adapter has frayed, get a new one, confirm with someone else's adapter.
Overheating related power downs, laptop power down when hot and within seconds/minutes of booting.
Open the laptop and clean the fan and its related wind outlets.
This needs to be done once every six months (at least).
Dear reader, If you are reading this please share your other hardware related diagnostic and trouble shooting experiences with this legendary laptop. It is useful if the last remaining dell inspiron 5150 to have a handy troubleshooting guide. like how would I know if my graphics card or processor goes out next.
also see
http://support.dell.com/...
Tell-me-how service manual, owners manual