You don't *INSTALL* a router either as hardware or software in a PC. It is simply a network device to which the PC connects, either by ethernet cable or wirelessly. It won't appear in Device Manager and it won't appear in the Network Connections folder - the only connection shown will be the network adapter (Local Area Connection or Wireless Network Connection).
I cannot therefore see how using the Linksys router can have had any effect on the CD and DVD drives. Have you run System Restore back to before the problem arose?