Power Issue on Inspiron 1150

If the system has been overheating for a while, it is much more likely the mainboard has been damaged.  Even with a faulty fan, the system will power up unless something else is wrong.

Why do you believe the fan and heat sink are going bad?  I have had to repair my 1150 for two different things that are similar to the laptop turning off.  First, the laptop would quickly overheat and shut itself off but I believe it would last longer than five seconds.  I had to remove the keyboard, remove the EMI shield, and remove the microprocessor thermal-cooling assembly.  Then use a can of air to blow the pound of dust that has collected in the fins.  To complete the repair, wipe off the old heat sink compound on the thermal-cooling assembly and chip and apply a fresh thin coat.  Second, the laptop battery would sometimes not charge and the laptop would also sometimes not work with the power adapter plugged in.  Slight "wiggling" of the plug would have an effect on the laptop power light.  While the laptop is off, plug in the laptop and look for the green light all the way to the right to come on.  In my case, that green light would intermittently come on depending on your slight wiggling skills.  In this case, the laptop could go out after five seconds depending on how much charge is on the battery.  To repair the laptop, I had to resolder the power jack.  Doing this requires a total disassemble to get the system board out.  When I flipped over the system board to inspect the power jack, it looked like someone was trying to save money on the amount of solder used on the power jack.  Anyways, I cleaned the area, applied a little flux, and applied a reasonable amount of solder to the power jack pins.  Voila, laptop is good as new.