ULN2002A Not turning on?
If you look at the datasheet, on the first page, under the heading of description, you’ll see that the ULN2002A is designed for 14-15V PMOS Logic.

Looking at the functional block diagram on page 2, you’ll see that there is a 7 volt zener diode in series with the base of the first transistor.
There’s no way that a 3.3V signal will bias that transistor.

They do offer a 5V CMOS logic version (ULN2003A), that will probably work for you, in your intended application.

Your confusion about ‘Von’ being 2V is because you were looking at the ‘test condition’ voltage and not the actual ‘parameter’, which is 13V. Look at the datasheet again. If you’re still confused, I can try to explain it in more detail.

Hope that helped!