Your burner is made by Lite-on. You might get better results by updating the firmware from HP, if one is available.
You probably just got a bit lucky with the first batch of Sony DL disks. They were probably a different type---different mid code than the latter ones, and the last ones weren't particularly compatible with your drive.
The only double layer dvds that we recommend are made by Verbtim. Either the 2.4x-6x or 8x varieties should work for you, though laptop burners are not particularly great burners, especially for DL media, and Lite-on isn't known as the best brand for burning DL in the first place. Still, the Verbatim would be your best bet.
I also recommend ImgBurn for burning anything, but especially for DL disks. If you are burning dvd-video, it will set the layer break properly where other programs fail. Try them at 4x first, if your drive will support that speed on DL media.