Ok 2 things i would suggest here ...
1. Try another appliance ( that is currently working ) thus eliminating the chance of a faulty power outlet.
2. Secondly, depending on the brand name .. some newer units seem to have a life span of 1 - 5 years, 5 if it was operated in the right conditions ( ie: not damp or dusty ) and considerably less if the unit was operated by children with curious or sticky fingers.
Now presuming the unit isn't brand new ( or you would have simply returned it for a warranty claim ) the next best option here is to consider that DVD players are quite cheap and inexpensive.
Ok so granted this is neither a solution nor a quick fix to your problem, but i trust you will consider keeping your fingers off the circuit board and away from the power supply for your own safety. Some larger components (ie:
capacitor ) store large amounts of power and touching them with a metal object may allow them to discharge to earth ... via whatever it is you may have in your hand at the time.
My advice, leave the cover on and take the unit to a repair shop for a quote.