All I've found for the Wired Auto Config missing in XP is that you get that service with SP3 - but that didn't sound right to me, although there were other suggestions to copy the key from an install disk or another XP machine.
As for the Computer Browser service, as a workaround, right click on it and select Properties and under the Recovery tab for the Subsequent failures, change that to Restart the service and for the two Restart boxes below that, set those to 0 - OK
The setting for the First and Second failures should also be set to Restart the service.
Close services and restart the computer to see if you get wireless connectivity.
To see if you can free up some space on the HDD, go Start - type disk cleanup then click on it or press enter when it comes up.
It will run once and then tell you how much space can be freed up, click on System files - OK and it will run again and may give a higher figure.
Open a Command Prompt and enter powercfg -h off followed by exit to close the cmd window.
This will turn off Hibernate but should free up a few GBs.
You'll be able to see by how much when you check C: before and after.
If that substantially improves the free space, then try the SP3 download again.
What is the history of the machine as to when wireless stopped connecting for your friend ?
I suppose it was unlikely after downloading anything with space being tight other than what may have caused the infection, but Windows needs at least 11% free space to work properly.
It's said that should be 15% but I've had a Win 7 laptop working with just 11% free - so I'm going with that.