Remote only turns on TV on second try

In order to turn on the TV using our Genie RF remote, we have to press the ON button once and then OFF, and then repeat the sequence. I replaced the batteries. Went through the process of pairing the remote to the TV again. But nothing seems to remedy the situation.

I also bought a new RF Genie remote, turned on the TV using the previously described two-step process,  and successfully paired that with the TV. However, I cannot get that remote to turn on the TV — it won’t even get the TV power light to come on.

Any ideas?  Is it the TV?