The purple 3500 stick was introduced in 2014, and was replaced by the 3600 two years later. Your 3500 is getting kind of long in the tooth, so it could have gasped its last breath.
The fact that you didn't get anything when tried on a different TV does make it sound like the problem is with the 3500. Just to eliminate the TV as the culprit, have you tried your other working stick on this TV?
Roku Streaming Stick +, 3810X, Ser YH0059427035, wifi - Samsung UN55ES6100
Roku Streaming Stick, 3600X, Ser 5S56D8240827, wifi - JVC EM37T