Yes I assume to the network name, you didn't answer the Yahoo search question.
You asked how this computer got this...I don't know, probably a drive by but cannot say for certain. What it was exactly was Trojan.Zbot here is some info on it:
One thing I would recommend is that you install, since you have been having continuing problems over the past few months SpywareBlaster on all your computers. It will at least keep out some of the nasties and also has a good restricted sites portion that keeps the user from even going to sites on the list. It's a great program, FREE, doesn't run in the background and does offer superb protection against spyware, adware, browser hijackers, and dialers. Simply download, install, update and then Enable All Protection and then close the program. Do this on all of your network computers. Manually check for updates weekly and when they have updates download, install and enable.
Also I would recommend that you update and run the AV program on all machines in the network and the same goes for MBA-M. Just to be sure all are clean.
Otherwise, looks good to me. If you feel all is fixed you can mark this one solved.