I wonder if you are using the correct power supply, or is it broken and not supplying charge to your laptop. If the battery is too low then this can also cause the effect you are describing - even with the charger working correctly. Also the battery could be faulty.
My advice would be to try removing the battery and use only the charger to power the laptop.
If this works then the battery could be either too low and it is drawing all the current that the power supply can deliver, or the battery could be faulty. Try leaving the battery in and the laptop on charge for a few hours and see if it works then. If it does then the battery will have been too low.
Finally, if all this fails a new charger that is compatible with your laptop (correct voltage and power output) may be needed. see if you can borrow one before buying one in case it has more serious cause.
Please let me know how you get on.
I really appreciate thank you messages as a payment for solving issues :o)