Don't have definitive answers but here are some things to consider.
My understanding is that using aprs-is requires your callsign and passcode to fetch data over the internet. Check to see if you can fetch data using an alternate channel such as APRSDroid if possible to verify your passcode.
Since the Kenwood HT is a D-Star radio it might be doing either D-PRS which sends and receives packets through a connected D-Star repeater direct over the internet to
aprs.fi (sending the aprs data over the d-star digital link on the repeater frequency) or analog APRS on 144.390 MHz in the US. I don't know which (or both) your radio does via the built-in TNC.
If it is analog you will only see packets that are transmitted by other radios over the analog aprs frequency. If there are no detectable transmissions in range then you won't see anything coming up on the screen.
You could listen to 144.390 audio and see if you hear packets in your area. Be aware that many fixed locations may transmit only on a periodic interval so there can be lengthy gaps between transmissions.
If the HT is only doing D-PRS then I don't know if the repeater will send out all local packets received by aprs-fi or not since I don't have any experience with D-PRS.l so I'm not sure what you should expect to see via D-PRS
Daniel (AE4ON)