Suggestion
I haven't had this problem on this particular product, but if you have a tester you can test the power supply and see if it is working. It should be labeled with the voltage, current, and polarity so you should easily be able to find a suitable replacement for it if needed.
If the problem is not the power supply, and the unit works on batteries (which I have experienced before on other equipment), you can solder a new power jack onto the battery terminals and connect the power supply to that. It's worked for me and beats the heck out of batteries.
Just be sure that if you replace the power supply, you must match the voltage, the amperage (usually shown in milliamps) AND the polarity (which conductor is positive/negative). And if you add a jack, you must again match the polarity to that of the power supply.
Good luck!