The short answer
Your remote works, so the opener's motor and brain are fine. That rules out the expensive parts right away.
The remote and the wall button take totally different roads to the opener. The remote sends radio waves through the air. The wall button sends a signal down two thin wires.
When only the button fails, the fault lives in that button, those two wires, or a setting that's shut the button off.
This is one of the easier garage door problems to fix yourself. Most people are back in business for under $25 and fifteen minutes of work.
What's actually going on
In the field, four things cause this symptom over and over. A worn-out button, a damaged wire, a loose terminal, or lockout mode.
The button is the top suspect because it's a cheap plastic switch you press thousands of times a year. Eventually the contacts inside stop making solid connection.
The wire is next. That thin bell wire runs up the wall and across the ceiling, held by staples every couple of feet. A staple driven too deep, a corroded splice, or a screw from a wall shelf can break it.
Loose terminal screws are sneaky. The wire looks connected, but a half-turn of looseness or some green corrosion on the copper is enough to kill the low-voltage signal.
Lockout mode shows up more on newer openers. If a smart panel's lock got pressed and held, it can disable button operation until you clear it.
The rare case is a dead terminal on the opener's logic board. Since the board also handles the radio and motor, and both of those work, board failure is unlikely (but not impossible).