This sounds like the unit may be running on its battery and the battery is running low. Is the orange light also blinking? (The LED is on the side near the worklight so it's easiest to check if the light is off.) First check if the power is on to the house and then to the garage area. Next check if the garage door opener is plugged into the outlet. Make sure that the battery is properly connected to the wiring harness (and the opposite side of the harness is fully seated as well).
If the LED is red and the unit is beeping, then replace the battery for the opener. The battery kit is part 41A6357-1 for the WD962KD Chamberlain Evercharge model. The Chamberlain 4228 is a substitute battery kit and is available at Amazon and other vendors. It is a little harder to put in the opener (and then remove later).
If a new battery doesn't solve the problem (after 48 hours of charging), then the opener's recharging circuitry has failed and can't recharge any battery. Depending on the age of the opener, you may be better off replacing the entire unit.
The manual for the WD962KD opener is available from Chamberlain here:
http://www.chamberlain.com/doityourself/pdfdocs/114A4249.pdf .
Please add a comment with your garage door opener model or check your manual to get the correct battery for your opener.
I hope this helps.
Cindy Wells