I've not had the best experience with the little SD205 and SD208 models from Linksys/Cisco...having to replace several dozen of them over the years. The symptoms of them beginning to fail is what you're experiencing...yeah the link lights may show things look good...but link lights aren't really a good indication of anything that something is plugged in and 1 pair of the ethernet has conductivity.
Try testing it with another set of good patch cables that uplink it to your router or whatever else is providing DHCP....and use a fresh patch cable to uplink another device to it. Power cycle the switch, power cycle the switch/router on the other end of the uplink. Connect a device to your switch..see if it will pull an IP from DHCP, (as long as you can confirm DHCP is working on the primary device)....if nothing...toss that and replace.
In this price range...DLink makes a nice little very inexpensive 8 port gigabit switch...something like 35 bucks.