There are a few reasons why the Famicoms might not be working for you.
The easiest thing to ensure is that both the contacts of the game cartridge, and the pins in the connector are clean. Games will not boot if there is not a good connection with the cartridge contacts.
What kind of power adapter are you using? Famicoms require a 10v DC 850mA, centre pin negative power supply. NES consoles output 9V AC, which can cook the Famicom system since it does not have circuitry to adapt the AC current to DC. Most commonly, people will plug in an AC adapter, and this will damage the LM7805 voltage regulator. These regulators are a very common part in older electronics and are still easy to find through places that sell electronic components.
Another reason for not getting a signal from the system’s RF out is that it outputs signals in the NTSC-J format, which differs from NTSC (and PAL, SECAM, etc). Channel 1 and Channel 2 listed on the RF output switch for the system which roughly corresponds to channels 95 and 96 on NTSC televisions. It is possible that your televisions can’t pick up this signal even if it is set to these channels.
To fix this, you can try to AV mod the system. This basically has you build a simple amplification circuit for the video and audio signals produced by the system, and output them to RCA jacks, which you can then run to your TV, or through an RCA to HDMI adapter to a TV/monitor.