from all indications the software says it has removed all of the problems.
This worries me.
Remnants of malware is the most likely cause of this issue if the malware created the problem in the first place.
However a lot of times the malware itself that is gone could have made changes to your system that are giving you the symptoms, so,
If I was certain the machine was absolutely clean of all malware.
The first thing I would do is re-install the drivers to the LAN or WLAN card.