Josh,
you need to look at two things:
*On your PC look at the Internet Protocol (TCP/IP) and check if the setting is Dynamic or Static. My guess is, it is set to Static, and therefor if another PC on the LAN has already a specific IP Address allocated (it may be Static or Dynamic) and you fire-up your PC in question (which has an Static IP Address and happend to be the same), then you will have conflicting Addresses. In any case change the TCP/IP of the PC in question to Dynamic.
*Check the Router for DHCP allocation. Check the IP Allocation Range, is the range big enough, it should be able to accommodate all PC's on the LAN.
Check if the DHCP is Dynamic or Static. It (really) should be Dynamic.
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My recommendation is:
SET YOUR LAN ENVIRONMENT TO DYNAMIC ALLOCATION.
1-set your PC to Dynamic allocation. Shut down this PC and (important) unplug ALL cables and and let it sit for 20 minutes or so. Plug the cables back in. Restart.
2-Shut down the rest of PC's and unplug ALL cables. Set your Router to Dynamic DHCP allocation. Shut the Router down including the Modem and unplug all cables. Let it sit for 20 minutes or so. This will clear the ARP Stack and Allocated IP Addresses. (Do not reset to Factory Settings).
3-Plug in the Router and Modem. Start the Router and Modem. Lights will flash on the Modem and Router. Once they stop flashing, plug in your PC, and bring up the Router screen. It may take up to 20 minutes before the (Dynamic) DHCP allocation will show, and the Connection etc. on the Router log.
4-Fire up the remainder of the PC's and set ALL of them to Dynamic TCP/IP. Again the Allocation and Connection will take time to display.
5-Hope this helps you, I have done this many times.