740 outside door handles are prone to failure. There is a small plastic link that breaks. If this is the case, you may have to destroy the door panel to get to the mechanism. I don't know if it's possible to get the panel off with the door closed. If you can get the three clips out from the bottom you may be able to. It may be possible to go in through the speaker hole and trip the latch with coat hanger wire or similar. With the door open you can disengage the child safety lock, then the inside handle will work normally. Replacement of the outside handle is not too hard once the door panel is off. See the FAQ for door panel removal info.

The sticking trigger button, as Aye Roll mentioned, is another possibility, particularly if the car has seen much road salt. I had it happen with a tailgate latch button. It took repeated applications of WD40 to free it up.