Very strange indeed? Did you resolve this? If not, I suggest you record a macro so we can see what SlickEdit thinks is coming in.
Open a plain text file, then select the Macro > Record Macro menu item. Go to a blank line in the file and press the key(s) that are giving you trouble. Select the Macro > Stop Recording Macro menu item. A dialog will come up asking you to name or save the macro. You don't need to do that. Just click the "Edit" button on that dialog. You'll see a small Slick-C macro file that should look something like the following. (This is for typing a double quote followed by a single quote). Let me know if your macro looks radically different.
_command last_recorded_macro() name_info(','VSARG2_MARK|VSARG2_REQUIRES_EDITORCTL)
{
_macro('R',1);
keyin("\"'");
}