The thread is from 2009 but I will post it for the records.
If your inspiron 1501 won't even start up (black screen from the time you power it up) do this.
1. Unplug the AC cable
2. Power the pc on with just the battery and leave it there in the black screen for 20-30 min.
3. Shut it down, then power it up again and that should solve the problem (it worked for me).
It could be a mobo/ac/battery problem, who knows.