It is very hard to tell exactly what what point a machine will be stuck. It is best to generically oil every single movable friction point. Tammi I believe out of desperation I used break cleaner or xylene to get one unstuck. Those have to be used out doors nowhere near flame. spray some in a can - plastic will go poof - then brush on with a natural art brush. Do not leave metal over night with out re-oiling anything that stuff touches.
The gold you see on that needle bar is more likely dried on old oil not rust. Usually rust doesn't find its way into a joint because there is a protective coating of oil. If you try to force gummed up oiled parts to move you may have so many gummed up parts in other places that are being forced that something will move but it may not be what you expect or desire. You can tell the difference between rust and dried on oil by scraping on it just a little. Rust will be rough. Dried up Oil will feel gummy or oily of course. Oil will dissolve with solvent. Rust will not dissolve with oil or a solvent. It takes an acid like vinegar to dissolve the rust. If an acid is left on a rusted part the part will continue to rust even over night rust will grow. If someone put some kind of stuff to clean off rust down your needle bar then unless it had good coating of oil, you will have rust somewhere and the needle bar will have to come out and be cleaned of rust as will the sleeve it rides in. If you take out the needle bar you will need to reset it and time it. If you pry on the needle bar you could bend the needle bar. If you pry on the needle bar you will very likely have to retime it. I'm sure there is an Igor reading this. Note to Igor, use oil to do your work as much as possible. Use gentle taps and then big force as a last resort.