The drivers for optical drives are contained within the operating system and do not need to be updated. You will not find them as a separate download.
The firmware for your laptop drive may be a proprietary one, released by HP, and not the manufacturer of the drive itself, in this case, the drive is made by LG. I did not find an updated firmware for your drive.
The problem is more likely the discs you are using. I was hoping to see if ImgBurn could find the drive and recognize the discs.
You do not have to change the conversion/authoring program that you are using. Simply have it output to the hard drive instead of the optical drive. Then use ImgBurn to try to burn the video to the disc.
If you don't want to do that, try changing media. We recommend Verbatim brand discs (but not their "Life Series discs). Look for AZO on the label of the cakebox of the Verbatim brand dvds. Here is an example at Amazon.com: http://www.amazon.com/Verbatim-95037-to16x-Branded-Recordable/dp/B00081A2KE/ref=sr_1_11?ie=UTF8&qid=1365200150&sr=8-11&keywords=verbatim+dvd-r
You can also get high quality Taiyo Yuden discs online, like these: http://www.supermediastore.com/product/u/taiyo-yuden-silver-thermal-8x-dvd-plus-r-media-100 I prefer the TY 8x +R version personally, though it is hard to buy TY in small packages anymore.
And there are a couple of other things to try. I still advise downloading ImgBurn because it can do one of these tasks. Start ImgBurn, and select any of the options...Write files/folders to disc would be fine. Then click on Tools-->Filter Driver Load Order and remove any filters found there.
You can also try the Microsoft Fix-it tool for optical drives, though I find it virtually worthless: http://support.microsoft.com/mats/cd_dvd_drive_problems/en-us