The short answer
If your opener's motor runs but the door won't move, the mechanical connection between the motor and the door has broken somewhere.
The motor and its electronics are fine. Power gets in, the motor spins. Something between that spinning motor and the door itself gave out.
On chain and belt openers, the top suspect is a stripped nylon drive gear inside the motor head. Second is a trolley that popped off the emergency release. Third is a cracked carriage.
The fastest test costs nothing. Pull the red release cord, lift the door by hand, and see what happens.
What's actually going on inside
Let me walk you through what fails and why, in the order I'd check it in your garage.
The drive gear is the usual villain. It's a nylon gear that meshes with a metal worm gear on the motor shaft. Nylon is quieter than metal, but it wears, and after 10 to 15 years the teeth round off or strip clean. The motor spins, the worm gear spins, and the drive gear just sits there grinding.
You can confirm this in five minutes. Pop the light cover, remove the top housing, and look for white or gray plastic dust. That dust is your old gear teeth. It's the most common opener repair there is, and it's cheap.
Next is the emergency release. That red cord disconnects the door from the trolley so you can operate the door manually during a power outage. Pull it (or let a kid yank it) and the door and opener are no longer linked. The trolley slides, the door doesn't.
Then there's the carriage, the plastic piece that rides the rail and connects to the door arm. Cold weather and age crack these. When it breaks, the chain or belt moves fine, but there's nothing left to pull the door.
A snapped belt or a chain that jumped the sprocket does the same thing from the other direction: the loop won't move, so the trolley won't move.
And the one that trips people up: a broken torsion spring. When a spring breaks, the door suddenly weighs 150 to 250 pounds. The opener strains, hums, maybe reverses, and never lifts it. People blame the opener. The opener's innocent.