OK. Now start Windows in safe mode and wait till it loads completely. Press the eject button on your Samsung drive. If the tray opens out and closes immediately then in all probability it is a problem with the drive.
If it remains open till you press the button again, then one may have to assume that some software is responsible for the auto closing of the drive when Windows runs normally. You may have to run msconfig and try disabling anything the startup that may have a bearing on the drive one by one till you locate the culprit. It may be a burning program/player/services that are run by those programs.
Though personally I have not come across this problem, I have seen posts associating this problem with Winamp, Nero Essentials and Infrarecorder.
And wait for some other experts to chip in. May be they can throw some more light on this.