OK, disassembly is quite easy.
You need to remove the mode select button / stem. You do this by pushing on the small dimple (marked with the yellow circle) and then pulling the button out.
You can then remove the movement holder (white). You'll notice that on the 4pm position (the mode select) there is a hole rather than a slot. That's what is preventing you doing this at the moment.
Then the movement holder then lifts out easily. Then the movement can be dropped out of the case.
Be careful not to lose the contact switch to the buzzer on the inside of the caseback. This is easily dropped and lost.
I would say that if you're going to proceed you have to be prepared to make things worse (than they already are). If you're not, then stop now!!!
In order to get to the LCD display, you're going to have to remove the hands, and then the dial.
This is the trickiest part (unless you're going to take the whole movement apart). Again, only proceed here if you're confident.
If you damage the hands and/or the dial it's game over.
If you do proceed, set the mode to TME (so the mode select hand is at 12pm. When you put the hands back on, put this hand back on in the same position. If you don't, the mode you've selected won't match the mode the watch is actually in.
Remove the hands, then the dial just lifts off (its a press fit with two dial feet).
Then you'll see the LCD on one side (the dial and hands side) and the other will look like the picture above.
I can't remember whether you need to remove the metal back plate to unclip the LCD.
If you do, you need to remove the 5 screws (with green circles around) and then lift of the metal back plate.
Its worth going this far to generally clean the movement up (with rodico) and inspect things.
make sure when you clip the LCD back in place that the clips are fully engaged. If they're not, you will either get a blank LCD display, or one where only some segments are lit.
If you're not confident to do this, then send the watch for repair.