Q: Internet connection works only briefly after restart

I'm trying to help my Dad troubleshoot an issue with his iMac from across the country. He is running Yosemite on his iMac. I'm not sure of the exact model of iMac he has. I believe it is the last one with an optical drive. He uses an Airport Extreme base station purchased in the last year or two.

His problem at the moment is that his internet connection works for a short time after rebooting and then pretty quickly he can't view any website. He did have some adware garbage installed until very recently. I know Genieo was on his machine and he doesn't think he purposefully installed anything else. He installed adwaremedic at the suggestion of Apple tech support and said it deleted Genieo along with many other things, but his connection has not improved.

His internet connection and router seem to be working normally. He has no issues with his iPad or Macbook Pro. He has also tested the iMac using wifi and ethernet connections and gotten the same results.

Does this sound like a residual effect of the adware or something unrelated? Do you have any tips or links for getting this fixed? Thanks!