Well it still may be hardware but its looking like its the network side of things.
Is your ethernet LAN onboard or a seperate card ?
It may be worth trying another card if its a seperate one, theyre under a tenner from most places and it may be that its developed a fault or the drivers not installed properly.
Is this the longest you think its worked since you started having the problems or do you think it may happen again a little later ?
I know that you have done your av and adware scans but it could stil be something that tries connecting to teh net when you are online.
When you said you reinstalled your OS was that a clean install or did you just run it over the top of the old one ?
Sorry for all the questions but we seem like we may be getting somewhere at last and I dont want you to have to buy a new pc or any other parts unnecessarily