The issue is certainly network related.
I'd start by firing up a web browser and pointing it to your PBX.. perhaps port 5000 and the /management/ URI. If you get nothing there, network/connectivity issues.
First thing, you need to route the two VLANs.. else the computers won't see the PBX.. or the handsets won't.. whichever ones are on the "other" VLAN from the PBX machine.
Routing VLANs varies with your network config. Poor man's method would be to use two port-based VLAN ports and hook the wire between them.. but that is effectively just a bridge.. and starts to diminish the returns on splitting them to begin with.
IMHO, splitting VLANs for the voice traffic still seems overkill.. whether small business or frankly a C corp. Voice needs some quality, but certainly doesn't demand huge throughput. I find the fabric needs to be up to snuff in general.. people want their voice calls to sound clear about as much as their YouTube videos to flow smoothely.

Again, just an opinion. In the end, the PBX needs to run connections to both VLANs in whatever fashion you choose to do so. I would "not" suggest multi-homing the PBX for both VLANs.. there doesn't seem to be enough granularity to configure adapter/address bindings for the PBX services.