Has the switch been configured? If it is straight out of the box then all the ports are on the same VLAN and all of them can talk to each other already.
Added by routing and switching expert Sudhanshu Gupta:
You need to have VLANs configured in the switch so that the switch can route packets from Network A to Network B. Also when you say that the switches are connected in a serial manner, do they have dual network interface cards (NICs) so that you are connecting them like so: PC1Interface1 connects to switch, PC1Interface2 connects to PC2Interface1, PC2Interface2 connects to PC3Interface? If this is the case you need to do teaming of the interfaces so that they have a virtual IP, and the same IP acts as the default gateway of the next PC down the line. At the same time you need to have some routing on PCs so that they can do the routing/switching based upon the destination network.
I hope this helps.