Do you mean tray is not opening but if CD or DVD is inside then it works fine ?

Well, this is problem with many DVD writer, I guess in India we are provided with Cheap quality tray in optical drives, as I remember, I have one old imported CD drive ie. directly imported and was costly at that time.. that one is flawless till time.. even after so many years.

On the other hand I had to dump an year old DVD writer just because it was having problem in opening.

Basically, they are mechanism to separate magnet from the over ie. used to hold the disc get disturbed and drive won't open.

Well, I don't think there is any solution, either you get those pulleys replaced with some jacks etc.. or get new DVD drive as its not costly anymore. Repairing is not viable option because new very cheap now. I had one, I even sent to company service center, it came back repaired but problem was still there. Tried local mechanics and  there is no gain apart of wastage of time and money. So either keep a CD inside always or get new one.