Door lock not working properly

Okay, if I'm understanding you, it doesn't have a remote but does have power locks? You can lock and unlock it from outside with a key, but using the interior switch it will only unlock the door but pushing it to lock doesn't work. From that description it sounds like a bad door switch or the wire for the unlock side has broken. To get to the wiring to test it you need to remove the inner door panel. To do that you remove the screws in the order shown in the three pictures. Then lift the panel up and out. Now you have access to the wiring and the switch assembly. Testing is easy and requires only a short piece of wire. If you refer to the wiring diagram in the first image you can unplug the connector from the switch. Now with the key on you just touch the wire between pins 11 (ground Black wire) and 8 (unlock signal Blue wire) If the door locks cycle to locked the switch is bad and replacing it will repair the problem. If jumping it doesn't trigger the locks it's likely that the blue wire has broken in the door flex area between the door and the body of the car. Sometimes you can reach into the door cavity and get to the wiring to remove the rubber flex cover and access the wires, other times there are screws in the accordion that release it. Once you found a broken wire you can repair it by stripping some of the insulation back and soldering the wires back together, or a better repair is to cut the wires a bit shorter and put a new piece in there so the solder joints are not in the flex area. Then cover them with shrink tube to protect the wire.

This shows a few ways to repair the wiring:

https://www.youtube.com/watch?v=r7GlDBge_WU