There are several things that you have not told us that would help us to give you better answers. These things include whether the 2 static IPs are in the same subnet or are in different subnets. And where the DVR is connected? Is it on the same switch? Is it in vlan 1 or some other VLAN? And whether this switch is a layer 2 switch or a layer 3 switch? And if it is a layer 3 switch does it have routing enabled or not? It would be quite helpful if you would provide a simple diagram showing the relationship of the DVR, the switch, the router, and the ISP.
I do have some comments about what you have posted and they may or may not point to the issue that you are facing.
- on the switch you have this
ip add *live IP* 255.255.255.x
ip default-gateway *Live IP*
it makes it look like your default gateway is pointing at its own address. Is that the case? If so that is a problem. The default gateway should point to an address on the router (and that address should be in the subnet configured on the management interface of the switch).
- on the router interface fa0/0.1 you have this
encapsulation dot1q 1
which makes the router interface perform trunking. But it has only one vlan configured and that is the native vlan which in untagged. I would think it would be better to configure the IP address on the physical interface since I do not see any need for a trunk for what you have configured.
- on the router interface fa0/1.xx you have this
encapsulation dot1Q yyy
which makes the router interface perform trunking and implies that it is for some vlan other than vlan 1. But you have not shown us that the switch has an interface configured as a trunk.
HTH
Rick
HTH
Rick