Getting updates for PCG-2C1L (VGCLT38E)

Model PCG-2C1L (VGCLT38E) all in one, windows vista

I am working on an old PC, making sure everything is up to date. Normally I would make sure the Bios is the latest, and then do windows and other updates. I noticed on sony support that there are a few newer updates for drivers and other factory software, but no bios updates are listed. On the dozens of PCs I have looked at there have always be at least a couple of Bios updates during its product life, so this is unusual. Next I noticed that windows updates complains that it is not enabled, but that there is something called VAIO update. Before I jump in and try the usual windows updates fixes:

Are there really no Bios updates for this PC?
Should I still be able to run windows updates, or is the sony updates feature supposed to replace that?