I've run into some problem with JTable.
Really? I can't imagine... ;) JTable is always a problem. At least for me. Powerful, but difficult.
Off the cuff, you would need to determine this in your table model's isCellEditable method. So in that method you would need logic to determine if the selected cell is part of an existing selected row. The problem with this is going to be timing. Does the row get selected before or after this method gets called? If it happens before, then your logic will always be true, which is a problem.