Enable mute button on avaya - Avaya 4610SW IP Phone

Did you try

Mute 7 3 7 3 8 # (Mute R E S E T #). NOTE: Press the Mute button momentarily

My office phone is similar and it has a long volume button, as well as a mmute button on the lower right side, along with all the other buttons.

Which phone? You list a 5400 series. That has a mute button on it. Just press the mute button.

AVAYA 1608 I (RESET)
REMOVE THE CABLE AND RESTART THE PHONE ONE'S IT RESTART.
YOU WILL SEE THIS IN DISPLAY" *program" AT THAT MOMENT CLICK " * BUTTON ON PHONE"
THEN TYPE " 27238#". SO IT WILL SHOW THE SETTING'S OF PHONE THEN CLICK " # " UNTIL YOU REACH TO DISPLAY SHOWING " command" TYPE THE COMMAND AS " PRESS MUTE BUTTON AND CONTINUE 2723825327 # " THIS WILL REACH TO SHOW IN YOU DISPLAY TO CONFORM THE RESET CLICK "# TWO TIME" THEN IT WILL BE RESET.

First make sure headset/handset adaptors are not plugged into the phone

Press Select
Press Mute
Dial 68 (this will show the current setting)
Press * to change the setting
When the setting is at what you want press # this will save tyhe setting and exit programming mode

Hope this helps.

The Mic/HFAI button mutes the microphone when on speaker.When the light on the mic button is off the microphone is muted and vice versa.

Mute the speaker, mute the ringing?

No, that will not disconnect the caller. BUT, if you hit the headset button again, it will.
If you hit the headset button, you need to hit the switch hook to regain the call....

its broken may need to get a new phone

Press mute reset (mute 73738)