My apologies - I missed it - too many posts...
With the button pressed, the output from the 555 (UM2/3 - which is also UL2/13) should be HIGH and the output from UL2/12 should be LOW.
When you release the button, after a short period of time, UM2/3 (UL2/13) should go LOW and the output from UL2/12 should go HIGH.
So, if your logic probe indicates neither a HIGH nor a LOW when the button is pressed this indicates that the output from the 555 is not a valid logic level. Faced with this - I would measure the DC voltage on UM2/3 with the button pressed. Post back what the voltage is.
I suspect that both the 555 (UM2) AND UL2 are both faulty. However, it could also be UL2 affecting the output from UM2.
With UM2/3 LOW (UL2/13 LOW) this should make UL2/12 HIGH. Hence the reason I suspect UL2 is faulty (but, as I have stated before, there could be something after UL2/12 holding the pin LOW).
Either way, if the UL2/12 output is permanently LOW, this is holding everything in RESET, so you have to resolve this issue FIRST before moving on with any further fault finding.
If you replace UL2 first, then perform the test again to see if you need to replace UM2 as well.
Are the capacitors C19 and C22 electrolytics or tantalum beads? They could also be faulty - but this will only affect the subsequent timing of the 555 reset pulse.
Dave