I would power off the modem, router and the PC, power up the modem, wait, then the router, wait, then the PC. I would try a different Ethernet cable (the one you did not use when you connected the PC to the modem).

@ArcherC8 

Thank you for the advice, but this did not help. I have cycled the power with the modem and router like you said but same problem.

 

Also, I have tried many cables from the router and all of them can transmit 1000mbps. I have 2 100ft cables conencting my router to modem, as the router is in a seperate building. One cable is cat7, the other and the coupler are cat6. When I hook my laptop directly to the end of those cables, I still get 1gbps potential speed. 

 

When I look at the UI of the Archer A7, it says the WAN port is negotiating at 100mbps, but the LAN port is at 1gbps. I am very confused about what this means. 

 

Additionally, I went to Amazon for tech support and I don't think they understood my problem, so they just sent me a brand new router, and it is having the exact same problem. This all feels very silly now.

Strange but not silly. Cat7 and Cat6 should be fine. Look at the pins on the laptop and ensure one is not bent although connected to the modem works. Try connecting to different ports in the router and the other ports empty. Power cycle the router and PC between tests. Is your laptop Apple or Windows based? Is your firmware up to date? Did you update the firmware just before you noticed the issue? Any new devices added at that time? Are you using the power supply that came with the router? Any power cords running parallel to the Ethernet cable? Any other devices such as AP or extenders?