There’s a bug with Traktor where SOMETIMES - for some reason - the transport controls stop working. I have NO idea why it does it, only that it occasionally happens with pretty much every controller I’ve ever used, including HID ones like the S2/S4 and CDJs.
To fix it, I usually mess with the jogwheels while hitting a cuepoint, and usually that frees it up.
Usually its an incorrect audio setting that will do this, but if it happens to be music downloaded from ITunes (M4A file) then if you don’t have quicktime installed on the new laptop then Traktor will react like this
The lack of playback when you press Play with a track loaded is almost always a sound card issue. Reselecting the correct sound card, checking output routing, or reconnecting the sound card can sometimes fix it.