So I'm new to managing Samsung products, I've been spoiled by Cisco. I've got some problems that just are being a pain in the rear, Any help would be grateful.

Our newest issues are that no one can receive voicemails from outside calls. When you call the voicemail starts then hang up right away.
The second is that phones have disappeared out of the system so you can not call them by extension anymore. One of the main extension being the front desk.
Any other one with voice mail, I set up a new users phone and verified that the voice mailbox shows up in odsm but they still cannot get voicemails. So this issues is least of the problems for now.

Again any help would be very much a godsend. It's hard to find any good troubleshooting documentation for the Samsung Office serv 7400 model. The current version we are using is V4.80

Is the voicemail a Svmi 20e or svmi 20i?

Can they get voicemail from internal callers? What kind of trunks are you using?

Where can I find out which trunks are being used on this system? Also yes the internal Voicemail is working.

We have the SVMI-20i

Look at the cards in the system and see if there is a Pri card or a cot card if neither one is there it could be sip.