This question sound familiar. Although I have no exact knowledge of the devices you are using, it sound very straight forward. You need to make sure that the uplink port of you current switch is setup as a trunk port, then configure the two vlan on the new switch. Make sure you specify the native vlan as necessary. You will need access to your current switch. If a company installed it and you purchase the device, the device is yours to do as you please and they should provide you the password.
It seem the only thing that you are missing is making sure that the uplink port is a trunk port and that one of the 2 vlan is set to native. below is an example for a Cisco port set with 2 vlans for voice and data. You should be able to get it to work by configure the new switch up link port as trunk. The set the port that the phones are connected to like below. Don't worry about the PC the phone's port is a switch also (VLAN tagging).
!
interface FastEthernet0/3
switchport access vlan 20
switchport mode access
switchport voice vlan 100
srr-queue bandwidth share 10 10 60 20
priority-queue out
mls qos trust device cisco-phone
mls qos trust cos
auto qos voip cisco-phone
spanning-tree portfast
service-policy input AutoQoS-Police-CiscoPhone
!
Hope this help.
Good luck.