I just upgraded to a model 392ox fr a 2720x only reason was the 2720 would get the peacock channel. I was half way through the setup when the remote stopped working. I pulled power on the Roku and removed the batteries, I hit the home 5 times reset and that didn't work. I'm not sure how to proceed at this point if I could get peacock I would stay with the old one.
The 3920 has an IR remote, so make sure nothing was blocking the front of the Roku when you were using the remote. The 3920 does support using a WiFi Direct remote, but you'd have to buy it separately.
Dan Roku Stick (3600), Ultra (4640), Ultra (4670), Ultra (4800), Premiere (3920), Insignia 720p Roku TV, Sharp 4K Roku TV, Nvidia Shield, Windows 10 Pro x64 running Serviio and Plex on a wired Gigabit network.
The Roku model 3920 is the Premiere (the one in the Express form factor, not the one in the Roku 4 form factor). It contains an IR remote, which will control any non-Stick Roku device. It may be that your older remote is bad.
The model 2720 is the Roku 2 from 2013, which came with a WiFi Direct remote. It was essentially a Roku 1 (model 2710) with a Roku 3 (model 4200) remote capability.