You've told us that your laptop will play CD-RWs burned on a previous laptop but not whether it will play your newly-burned ones. (You've only said that they won't play in a standalone CD player).
If they also play OK on your laptop then it would seem to be a compatibility issue between the discs and your CD player (rather than a problem with your laptop's CD drive or its burning software). In that case I'd suggest trying CD-Rs (because some CD players won't recognise CD-RW discs).
If the newly-burned discs won't play on your laptop, go to 'Computer' and right-click on the icon for the drive with the disc in it. Select 'Explore' and see if Windows can recognise any content on the disc. (There should be a single file, containing all of your tracks. If you see MP3 separate tracks you've burnt a data disc, rather than an audio one. If you see nothing at all there would appear to be something awry with your burning software. Try something different, such as Ashampoo's freebie:
https://www.ashampoo.com/en/usd/pin/7110/burning-software/Ashampoo-Burning-Studio-FREE ).