Your second option should be 'I have a problem with this'. And that leads to the difference. A problem means one particular problem. 'Trouble' is used for more general situations, perhaps with multiple problems. 'I have a problem with this window'. The catch is broken. 'I had trouble with that window'. The catch is broken, and there is paint all over the glass. 'Bob always has trouble with his car - it keeps breaking down. He needs a new one'.