Panasonic DECT 6.0 always says "New Voicemail"

Call the service provider but if your provider is with ATT
this might be of help :
Resetting Voicemail Password

1. Reset Voicemail Password online at att.com.
2. You will receive a free text message confirming the voicemail password has been reset.
3. Press and hold the 1 to call the voicemail system from your wireless phone.
4. When prompted, enter your new secure 7- to 15-digit voicemail password, and then press the # key.
5. Follow the prompts to complete the voicemail password reset process.
6. You will now be able to receive and listen to voicemail messages.

You have unheard messages on the voicemail system provided by your telephone service provider. This system records messages when people call while you're already on the phone. Please contact your telephone service provider for instructions on accessing their voicemail system.

You have unheard messages on the voicemail system provided by your telephone service provider. This system records messages when people call while you're already on the phone. Please contact your telephone service provider for instructions on accessing their voicemail system.

You have unheard messages on the voicemail system provided by your telephone service provider. This system records messages when people call while you're already on the phone. Please contact your telephone service provider for instructions on accessing their voicemail system.

Apparently you're subscribed to a voicemail system offered by your telephone company. Please contact them for instructions on accessing their voicemail system.

you can contact the service provider.......

According to the manual you have to subscribe to your telephone service providor to set up voicemail.
"If you subscribe to voicemail service offered by your telephone service provider, New voicemail and appear on the handsets when you have new voicemail messages. Contact your telephone service provider for more information and assistance about using your voicemail service."
I have inserted the manual below
LINK
HOPE IT HELPS, ALAN

You received a message on the voicemail system provided by your telephone company. To hear the message, dial the voicemail number provided by your service provider (in many cases, this will be your own phone number), and follow the voice instructions for listening to your messages. You need to store the voicemail access # by pressing [MENU], [#] [3],[3],[1] on the handset. To access the voicemail, press [TALK], then softkey [VM]. Depending on your service provider, you may need to clear your voice mailbox to remove the notification.

If your wife never reset the codes when she used the phone, the "unlock" 4 digit PIN code is usually 1234, or sometimes the service provider resets it to the last 4 digits of your cell phone's number before sending it to you.
The SECURITY code is a 6 digit code which is set to "000000" when the phone is first sent to you and since your wife never used it that should still be it. I'd try entering 000000 for the "invalid security code" message you are getting and see if that does it. Some service providers may reset that security code before sending the phone to you too, so if any of those codes don't work you'll have to call your cell phone service provider to find out the codes. This info about all the codes was in my Razr V3 manual. Hope it helps.  If that does work for you and you can get into voicemail, then to reset the codes to your own personal ones go to ....Settings > Security > New Passwords and reset them.
If you get to the voicemail message screen and the message  stored there, (it's probably a message from the service provider) you have to call the voicemail number to retrieve the message, I just  press the keypad "dot" on the top right side under where it will say "call " and it dials & brings me to my voicemail.  The voicemail number should be stored in the phone, but because it was never set up you may have to call the provider to do so, I can't remember if it was already in there or not when I first set my phone up. Anyways......Good Luck & Happy New Year ; )