A [with wireless card internet access] knows about B but 'Network path not found'. B has full access to 'Public' on A but no internet access. This disappeared when A downloaded updates after using TDSSkiller.exe to eliminate 80072EFE. B was fully updated prior to losing internet.

Hi hanslip, Try to restore the computer to a restore point in time prior to the machine (B) getting infected. Personally, I would not trust "B". I would wipe the drive and apply the full system image backup created after the original installation.