Flipping between ham and gmrs (and unlocked) modes shouldn't break anything. One of my two GMRS-mode radios is a ham model, and my ham radio is a GMRS model. (Why? Because I wasn't paying attention when I was setting modes and I'm too lazy to swap antennas/modes, that's why)
Two of my four radios (one ham, one GMRS) are warranty replacements, and I have a fourth radio that's dead somewhere. All of them read 0W on an SWR meter but could still TX to a nearby (i.e. in the same room) radio after they died. Assuming you have all your settings correct (allowed frequency/channel, correct offsets, etc.) and still can't talk or it shows 0W, send it back or contact TIDRadio support and have them ship you a replacement. Or get a different radio. I think I'm done buying H3s after this and will be switching brands when my remaining radios start dying.