2004 Infiniti G35 RANDOM ISSUE

My car was inside a driveway for almost two years. It was perfectly fine before that. I would start it up on occasion just to keep the engine functional. I just recently got it on the road again and got the tires rotated. Then I noticed that at idle speed, the car would somewhat "lunge" forward but there was no engine rev so ive kind of ruled out a possible mechanical issue. At higher speeds though, there would be a shake/thump and perhaps a slight wobble from what seems to be the back tire(s). I got the tires changed out for some really good used ones as I thought this might be the issue. It turns out it wasnt so I took it to get one of the rims straightened out because it was bent and still no positive results. I then took it to my family mechanic and he lifted the car and had me hit the gas a few times to check the roll of the tires and after looking at it for a while, he suggested it needed a wheel balancing BUT the guy I got the used tires from had "balanced" them already. I just need a second expert opinion. Im exhausted at trying to find a solution or a possible diagnosis. Please help.