The very first thing I'd check on is whether the TVs require a converter box or if there's already a built-in ATSC tuner, found on most HDTVs. If not, the switch to the digital signal means your TV won't respond to anything, let alone a system hookup, without a converter box.
Did you firmly plug the AV cords and power supply from the system to the TV or are you relying on off brand junk like those RF switches and AC adapters "designed for N64?" (which is sure to get you nowhere) I'd stick to official Nintendo brand parts.
If you've tried everything, your TV's or systems and parts may be defective. Unless your TV's only conflict with your system, you can always get new ones with some sort of warranty or exchange.
I recommend getting converter boxes. My dad has a Westinghouse LCD TV that still needed one, so that could be it.