The starter motor recently went on my mk3. I fitted a new starter and the car now starts every time but seems hesitant when starting from cold. The first time I start it in the morning it makes a whirring sound for a couple of seconds and then starts. It does the same thing if it has been parked up all day. However once its been run once it starts fine every time with no funny sounds and no problems, even if it has been parked up for 2 or 3 hours. I wondered if this could be something to do with the new solenoid/starter although I'm not sure why it only does it after the car has been standing either all day or all night. Other than this hesitancy when starting from cold, it runs and drives perfectly whether the engine is warm or cold. Any suggestions would be most appreciated.
Check all your starter connections - tight and no corrosion, as mentioned above check your battery and it's connections (again tight and no corrosion) and confirm that your alternator is charging the battery sufficiently and while your at it check the alternator connections as well. Is the starter still under warranty? If all of the above finds no issues then it may be worth considering a return under warranty or another replacement. The only other thing I can think of is that while the car is not being used, you have an electrical current drain that is weakening the battery strength and in turn may be putting too much of a strain on the starter