I had exactly the same problem last November with an old Dell D505 laptop.
After you boot, before it shuts down, try looking carefully at your screen from different angles.
Can you very faintly see the desktop? So faintly you almost have to use your imagination to barely see it?
In my case, I first tried replacing the power transformer cord, thinking a small wire in the cord might have been broken preventing proper recharging. That did not fix the laptop's problem.
Next I replaced the motherboard & video card. That also did not fix the problem.
Finally I replaced the monitor screen, which instantly did fix the laptop problem Backlight had failed.
Glad I had bought a 2-year warranty which covered the new parts from Dell.
I have to mention that Dell's service to me was FANTASTICALLY good; probably the best service I've ever received from any company for any product in my entire life.
Indication: most likely your screen's backlighting has failed, requiring monitor screen replacement (which is a simple task).