That 2010 model had "internet@tv" and well, most folk would not call that "the interenet."

Are you writing you had 3 years and never got it to work? Ouch. At this point I won't bore you with trying to fix your TV internet connection issues.

The HDMI cable should be the best but I'm encountering folk that can't make that work today. Usually it's some setting on the laptop but since you've been at this for 3 years, the best advice I can give is to get some help locally.
Bob