The fact that everything is functional using the remote control, and that both door switches unlock all the doors but don't lock any, narrows down the possibilities.
The switches control the lock/unlock by grounding a particular terminal (one for lock, another for unlock) at the keyless entry module connector. (The remote system doesn't use this same wiring.) Because the switches work for unlock, we know that both switches are probably good, and their common grounds are good (otherwise they wouldn't work to unlock either).
That points to two ideas. The first is that both switches have failed on the lock side only. Not likely, but not impossible. (The spray cleaner idea might help with this.
The other is that there's a bad connection in the "lock" wiring between the switches and the module. It could be just a bad contact at the connector itself.
Perhaps start by locating the module and removing and reattaching the connector(s). If that doesn't work, then, with the connector off, measure the resistance between the "lock" wire and ground. It should be open circuit when the switches are in the neutral position, and close to zero when they are in the "lock" position.
Armed with the wiring diagram, you could unplug the switch and place appropriate jumpers into the plug socket. This will eliminate the switches as well,....if you don't have an ohm-meter to do @plain OM's test.
According to the FSM, the keyless entry control module is behind i.e., forward of) the glove compartment. The glove box has to be removed for access. The module should visible, and is held in place by a single bolt. It might be possible to access the connector without actually removing the module.
The connector at the module is identified in the wiring diagram as B176. At the bottom of the diagram there is a drawing of connector B176. This is the view when looking at the harness connector after it's removed from the module. In other words, it's face-on, with the locking tab on top. It's a a long rectangle with two rows of terminals.
The two wires/terminals of interest are #5 (white) and #15 (green with red stripe). I don't know which is for the lock function and which is for unlock. But it should be easy enough to identify by measuring the resistance from each wire to ground while moving the switches from Off to Lock, and Unlock. If the problem is in the wiring or switches, one of the two wires will be grounded when either switch is moved to unlock (we know unlock works), but neither wire will be grounded when either switch is moved to lock.
If the switches and wiring are good, then both wires will be grounded by the switches at the appropriate position. If reinstalling the connector on the module doesn't restore full control (just a bad contact between the connector and the module), then the problem could be in the module itself.