Got a 1984 System 3

[andy]

To add channels, enter the channel number and hit enter on the keypad on the TV (not the remote).

Try removing the antenna switcher to see if that's causing the snowy channels. You only need it if you're using several antennas, or an antenna and cable. Try connecting the cable to the UHF input if it has one. TVs with separate UHF and VHF inputs need to have the cable signal going to the UHF input for channels above 65 which are in the same band as UHF. 80's Zeniths also had bad soldering in the tuner under the shield. I had to resolder every one I saw to avoid intermittent snow.