The power drops off at the IP solenoid once the ignition is turned on. I've proved that with my ALH Van and my 2000 Jetta. The power (initially 12+ volts) will rapidly drop to less than 2 volts when the ignition is turned ON (I have photos for documentation). Thus, turning ON the ignition walking out front and placing a multi-meter on it to check voltage will give you a false reading/impression.
The Solenoid (N 109) receives it's power directly from the ECU, Pin 121/120. If you jump power to the Solenoid without disconnecting it, current will back-feed to the ECU. This procedure can "by-pass" an electrical issue back upstream, thus, possibly allowing the engine to start.
The Actuator doesn't come into play with starting the engine. Without vacuum, it is not going to move anyway. Once the engine fires and there is vacuum produced by the pump, the Actuator arm is pulled down fully against the set-screw. But, none of this has anything to do with the engine starting properly.
You need to confirm whether or not all three of those Fuses (32, 34 & 43) have 12 volts. All three of them provide power to "key" components with respect to starting and running the engine as outlined in my initial post!
When you crank over the engine, if the RPM (Tach) shows zero, then, the sensor is most likely the culprit as Oilhammer indicated. The Engine Speed Sensor (RPM) is located below and to the right of the Oil Filter Housing on the block near where the transmission mates to the block. The wire leads up behind the IP and plugs to the big wiring bundled there. Other than observation on the Tach, I do not know of any way to test it. However, if certain parts of the ECU are not getting power due to one of the Relay 109 circuits being bad, then, the RPM sensor may not function.
Again, I say do the simple first.... check the power coming off those three fuses !