Try use a brand new cable rather than trying cables you have at hand.  I assume there ought to be two cables at minimum in the connection. One from cable modem to router. The other from router to 3891.  Both cables need to be replaced with brand new ones to see if there is improvement. when you say you have confirmed 1gb speed straight out of modem, did you try connecting 3891 directly to modem without a router?  You can test the cable that way too, although such a connection is not recommended due to security risk.  If you try that do it very quickly then disconnect.  
I am only receiving 80-100 mbps download speeds (60 mbps Upload) on my Dell Inspiron 3891, purchased approximately one year ago.... I have confirmed the speed coming out of the modem is 1gbps. I have a Google Nest wifi router connected to the modem.  My system says it has a Realtek PCIe GbE Family Controller. I am assuming that would allow me to obtain up to 1gbps ethernet speeds. Can anyone ID why my ethernet speed is so slow? I have Cat 6 ethernet cables....   Thank you!
Slow Ethernet - 80-100 mbps on 1gbps internet service