Car recently started to feel very bad. Lately, the car will not WOT at all, i can hear the engine trying to rev and all but the transmission will not go. The RPMs are going upwards towards the 3.5-4.5k and not shifting at all. Car drives perfect when driving hard. It can accelerate normally, but if I want to take off, nothing happens.

Other symptoms:
1) When I come to a stop, car idles below 600rpms and it feels as if it wants to stall, no shudders or anything, as soon as I stop it dips below 600-500rpms but doesn't stall or shudders.

2) I get a violent vibration going into and coming out of 4th gear, I don't know whats going on here, but this has been happening since I got the car a few months ago.

3) Tiptronic system does the same, very hard to WOT or accelerate on a dime.

Any ideas what this can be? I am going to get the check engine light checked out tomorrow, but I was hoping with these systems you guys can let me know What MIGHT be wrong with the car.

Btw, its a 3.0L Sigma Engine, 2001 Hyundai XG300. Thank you!