I'm not sure what your problem is, but you should be able to give all of the computers connecting to the router fixed IP addresses so that there won't be any conflicts.
If addresses are allocated automatically by DHCP, it is possible to put a PC into Standby without it releasing its IP address. If a second PC is booted, the router (being unaware that an address hasn't been released), may give that same address to the second PC. When the first PC resumes from standby, there is an IP address conflict.
If the Linksys router performs well "wirelessly" throughout the house, keep it and get the IP addressing sorted out.