Interesting. Can you elaborate on the operating systems used for those two computers and perhaps the dhcp lease assignment details for each. What is the time interval between the two computer uses? FYI, dhcp clients typically issue a renewal at half-life of dhcp lease. Also, dhcp clients upon boot-up, typically request their current dhcp ip (what they had at their last shutdown) as part of their discovery request to the original dhcp server.
My thoughts at this time to potentially explain the dhcp ip conflicts with these two existing LAN clients is that maybe the dhcp interval lease time has been exceeded on the dhcp server and when the offline clients startup they use their out-of-date lease(s) before acquiring a new one from the router's internal dhcp server.
Another thought that could cause this issue is the rebooting of the router which would cause it to not retain its previous dynamic leases it handed out to local clients. So, if client A received 192.168.0.100 as a dynamic lease from the router at a point in time. Then, router was reset somehow before client A renewed its lease, the router could assign out the beginning of its fresh client dhcp pool to client B having the same 192.168.0.100. Most dhcp servers will attempt to ping a lease before assigning one out to help avoid ip conflicts with pre-existing or rouge clients. If firewall rules or equivalent on the local client(s) prevent the dhcp server's preventive ping check then the dhcp server could easily hand out conflicting ips.