Just purchased my first sewing machine, needle not in centre of presser foot

[Monolithic 0]

I decided to try my hand at rigging so I just picked up a Singer 20u73 used. The guy claimed he bought it in 2007, used it for a week and decided it was too fast so it sat since then. I would like to say I believe him because the machine/table appear in perfect condition, no real wear at all. http://imgur.com/a/gS4FK

Anyway, so when I put the needle position to centre with the plastic slider, the needle is slightly off centre to the left. It actually very slightly hits the inside lip of the presser foot before going down. http://imgur.com/LJzVl2x

The slider doesn't appear to be centred either. I took three pics of each position.
Centre: http://imgur.com/m5Y6jmg
Slider to the right (so needle left): http://imgur.com/BiY8gwp
Slider to the left (so needle right): http://imgur.com/5JXKxqP

I couldn't actually even put the slider in the left position until I took the top off and backed off a screw that appears to be a stopper for the slider position. I tried fiddling with heights of the two stopper screws, but didn't make any headway for the centre position of the needle.

I desperately want to just start adjusting stuff and see where it gets me, but thought it wise to check here first. And I realize I could just take it to a shop, but CSPA rigging requirements say you'll be tested on machine maintenance so I might as well learn now.

Cheers!

[gowlerk 1,929]

Singer 20u adjustment manual is attached.

Always remember the brave children who died defending your right to bear arms. Freedom is not free.

[Monolithic 0]

Thank you! I saw this manual mentioned in another thread and looked everywhere and coudn't find it. I will try this this evening.

[gb1 3]

You might be able to release presser foot rod tension and rotate presser foot to center needle. Presser foot should be parallel with throat plate.