2 LANS on one switch?

Best guess these are cameras (and some recording software or a DVR) from GW Security. 

45/55/85/125 Series IP Cameras Information & Downloads

Can't provide relief related to the need for configuring  your PC to the 192.168.x.x network and some unused IP address. From that  PC you should be able to login to the camera with the admin admin credentials.

Good part at least is that this business appears to be still active, has a support channel, an address, and last but not least some support phone number. 

Alternate approach would be to figure out why your LAN is on a 10.0.x.x IP subnet. More labor intensive would be to reconfigure the complete 10.0.x.x network (and probably many devices) to the more common 192.168.x.x IP subnet. One possible reason for that other network could be that your router (again an unknown make and model) is connected to another router-like device like a cable modem with a built-in NAT router, which is already on the 192.168.x.x IP subnet.