Just because the TV gets internet, it does not mean the cable is ok. A badly crimped cable can work with reduced throughput - if you've not already done so, i'd definitely try it with another one.
I assume the TV has wifi too - can you hang an access point off the switch and see what speed the TV gets via the speed test on wifi? Unlikely, but could be a dodgy ethernet port on the TV. Not sure it will tell you much, but it's another data point and could also rule out any ISP throttling as suggested by BitPipe.
If you can't get wifi to it, set up your phone as a hotspot and see if it works with that?
Did you try a web based speed tester (as per the link i added above) rather than a downloaded one?