Bluetooth headphones won't connect
Most Bluetooth headphones only remember one active connection. If they're paired to your phone and your phone is in the room, they'll keep grabbing it — that accounts for a large share of "won't connect" cases.
Disconnect them from everything else
Start here. Most headphones hold several pairings but only one live connection, and they reconnect to whatever they saw last.
Turn Bluetooth off on your phone and tablet, then try the computer again. If it connects instantly, you've found it — check whether your model supports multipoint, which allows two live connections at once.
Put them in pairing mode, not just on
Powering headphones on is not the same as making them discoverable. They need to be broadcasting before anything can find them.
Usually: hold the power button several seconds past the point where they switch on, until the light flashes two colours or a voice says "pairing". Check the manual — the button and duration differ on every model.
Remove the old pairing before adding a new one
A stale entry blocks a fresh connection, and the symptom is a device that shows in the list but never finishes connecting.
Delete the headphones from the computer's Bluetooth list — Remove device or Forget — and pair from scratch rather than clicking the existing entry.
Check they aren't just the wrong output
"Connected but no sound" is an output-routing problem, not a Bluetooth problem.
Open your sound settings and select the headphones as the output device explicitly. On Windows, also check the app itself — the volume mixer lets individual apps use a different device from the system default.
Cut down the interference
Bluetooth shares the 2.4 GHz band with Wi-Fi, microwaves and USB 3 ports.
If audio stutters when you're close to the computer, try a different USB port for the dongle, or a short extension cable to get the adapter away from the machine. A USB 3 port sitting next to a Bluetooth adapter is a well-documented source of interference.
Charge them fully
Low battery makes headphones behave strangely long before they die — dropping connections, refusing to pair, cutting one side out.
Before going further, charge them to full and try once more. It's a boring answer and it's right often enough to be worth doing first.