[XCNuse]

The one thing that controls most about a start is the battery. If the battery isn't strong, there will be a very sluggish start.

This makes perfect sense to me at least, especially if you've never touched it.

If it's a hard start, but when it warms up and is at a normal idle, the oil is warm and easy to move, so the second start, even with a bad battery, is easier for the motor to move around. When the oil is cold, it's a lot more harsh on the starter to get everything moving.

 

[XCNuse]

At this point... no. But you've done well over anything else I would've done. Personally I would've started at the battery as most slow starts are related to the battery as it direct affects the strength of the starter motor.