So two computers, only about a year difference in age are getting significantly different speeds using the same wired connection. One computer gets between 80-100 mbps download, the other gets 1-30 mbps download. The slower computer is clean of malware (I used Malware Bytes). The problem is not the cable because I used the same cable for these tests.
The slower computer is an HP ENVY m6-1105dx Notebook PC, running Windows 8 The faster computer is a Dell Lattitude E6430, running Windows 7.
UPDATE: When I rebooted in Safe Mode, my connection was about twice as fast, using speedof.me as a benchmark.