Do I need a new part?

Something must have come undone mechanically. You will need service unless you want to try and strip the machine to look for it.

you have a fault no one else has

https://www.google.com/search?q=Elna+Contessa+320+presser+foot+won%27t+lower+far+enough+to+reach+material

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Check the latch component on the presser foot bar and on the presser foot. Perhaps something has become loose, fallen off, or become damaged. Have you tried a different presser foot and, if so, does it work? If more than one presser foot will not attach, then the problem is on the presser foot bar.

It is most likely the presser foot you are trying to install was not made for your machine. There are so many machines available and most of those machines have their own presser feet, which are not interchangeable. Unfortunately, even a Singer presser foot is not interchangeable with other Singers. Some have screw attachments, others have lever attachments, some have long shanks, others have short, some are straight, others are slanted. You need to figure out what style presser foot your machine takes and then search for either the presser feet that fit or a shank adapter that you can then use snap-on feet (kits are available on eBay).

http://www.sewingpartsonline.com/sewing-machine-presser-feet.aspx

Sewing Machine Feet eBay

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You need to loosen the tension on the machine. There is a dial that has numbers on it. The higher the dial is set, the tighter the tension is. Turn the dial to the left one number. Then try it. Do it over and over. Do not turn the dial all the way down or you will mess up your machine. Do it slowly, one number at a time and try the machine between dials.

Have you checked the screw on the side that holds the holds unit in place.? If not, tighten that. :)

Not sure what the problem is.

There is a screw that holds the presser foot shank to the presser bar.

When the presser foot shank is lowered, it snaps onto the presser foot.

See page 26 of the manual - http://www.singerco.com/accessories/manuals.html

It sounds as though you are missing the ankle which is the part the foot attaches to. The ankle attaches to the metal rod with a screw and the foot snaps onto the ankle.
sewman7

more than likeley the set screw is loose on the presser bar shaft ,remove the endcover and take a look should be simple

The presser bar is not moving, there is a set screw that controls the presser foot height on the bar, it may be to tight. Take the side cover off, and look for the presser bar, the set screw unit should be facing you. Unscrew it and see if the presser bar handel will now move.

The presser bar height should be set at 7 mm. To make an adjustment loosen the set screw. From the top of the machine, press down firmly on the presser bar and then secure the set screw.