I just got a 32" Dynex HD TV. I set the system using my old set top box and old remote (non-HD). When I used the TV button and the off button, the TV turned off, but if used the STB button and then the off button (I programmed the remote to turn off both the box and the TV) both would turn off, but then the TV would turn back on. I replaced the STB with a HD version and it came with a new remote. Now, with it programmed to turn both off when I put the STB button - the same thing happens - both turn off but the TV turns back on. AND the same happens when I push the TV button - TV turn off then right back on. Whats up with that?? I am using the Dynex code of 0495.
The control of the TV via the Verizon remote is best case and does not work with every brand or model of TV unfortunately. Dynex is an off brand made by another major vendor so various codes may work but not all functions for a particular model. The code you are using sounds as if it only a partial match. Try using code 0490 or or 1490 which have also worked for certain Dynex models and let us know if that works for yours.