The 1N4148 used to protect the transistor is a small signal diode and is probably not the best option. I'd use a 1N4001.
The diode would probably fail short circuit which would then take out the transistor, followed by the 555 (U1). You've said the motor still works in some respects, so the diode likely hasn't failed, and the fact that it's not on all the time probably means the transistor is OK (If the motor only turns off when the pot is at one extreme end, this is because the motor is being shorted out by the pot and the damaged 555, however I don't think that's what you observed.
Just to be sure,remove the motor and the power from the circuit and use your multimeter on the ohms range to read the resistance at the following points:
- Across D1 (both ways). The resistance should be significantly higher one way than the other. If your meter has a diode test range, it will typically read 0.6 one way and OL the other way.
- Across the transistor T1, again both ways. The resistance should be high (tens of kΩ or higher)
- From pin 3 of 555 U1 to the positive and negative supply rails (or pins 1 and 8). The resistance should be in excess of 1kΩ.
- From pin 7 to pin 1 of the 555 U1. It should be a high resistance (greater than 10kΩ) but it is likely it is low (under 1kΩ) due to the lack of a resistor in series with your pot having damaged it.
I've tried to estimate resistance values that you'll get in-circuit regardless of most likely other failures. If you're uncertain, post a list of all the resistances you've read and I'll try to interpret them
It might also be useful to see the other side of your board so I can check for any obvious mis-wiring.