You're going to have to replace the keypad assembly, this is a very common problem in all the new series of instruments and the E19xx series of meters.
Price isn't too bad and you can find them for much less on Ebay.
Richard
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Hello,
I have agilent E4416A series power meter. the voltages are ok 12v,-12v, 5v and the battery measures 2.9v the stand by light is on but when I press the power button nothing happens you can help me and thank you in advance.
Best regards