What arrow keys? the arrow keys do not, normally, move the cursor from field to field (they normally move the cursor through the text inside the field.) It sounds like you have an OnLayoutKeystroke or OnObjectKeystroke script trigger responding to the press of an arrow key to move the cursor to the next field. That script should be modified to not enter these fields.
You could also use merge text with these fields to keep them from being enterable. In layout mode, click with the text tool where you want to put the field and then use the Insert menu to insert a merge field.
"OnLayoutKeystroke or OnObjectKeystroke script trigger"
You have it one. Thanks
OK the solution (thanks to PhilModJunk for the pointer). It was an OnObjectLayoutKeystroke script that caused the problem, using Go To Next Filed or Go To Previous Field. The solution is to amned the layout field tab order to remove the non-enterable fields form the tab sequence by setting their Tab Order number to zero.