If your manufacturer is out of business, you are not going to find any BIOS updates; it's that simple. Your laptop is 6 years (and 6 processor/chipset generations) old; it's probably time to start thinking about replacing it. Perhaps, at this point, the question is: What you are looking for in a BIOS update? Most manufacturers will release a few updates here and there if bugs are uncovered in their BIOS; it is rare, however, to see any provide feature upgrades.
Sadly as N.Scott.Pearson mentioned if the manufacturer of the product is no longer in business we are unable to get BIOS updates for it. Now, if you are looking for other downloads you may try the ones that appear on the link below:
https://downloadcenter.intel.com/product/81508/Mobile-Intel-965-Express-Chipset-Family Intel® Download Center
Based on the research it seems that the motherboard you have has a G965 express chipset, and that link contains all the available downloads for that chipset (it does not include BIOS updates). Bear in mind that the drivers that appear there are generic and may not work because you have a branded system.
If you need more assistance please let us know.