[Darryl Ramm]

OK well now we kind of can work out you have standard (not a USB) headphone with a 3.5mm TRS phono plug and are plugging it into your HP laptop's headphone jack (actually a combo headphone/mic jack?).

AFAIK this jack is simply connected to the same audio device as the laptop speakers. The speakers should be muted when you insert headphone plug into the laptop headphone/mic jack. If you plug in the headphones and the speakers are not muted then its likely just a mechanical problem with the headphone jack (socket). That does not fit with what you say about this working OK for other applications. Try checking (look and feel) that the plug is actually going all the way into the jack and try wiggling the plug in the jack, try a different set of headphones. If the jack is faulty replacing them is likely not hard, and parts are available online if you are handy with a soldering iron otherwise any laptop repair place or HP or an authorized repair agent can do this.

If this is instead a software/ASIO4ALL driver/playback engine setting etc. problem it does not jibe with all you have described so you may need to go back over that and reexplain exactly what you are doing.

Darryl