I don't really have a problem, but cleaning. I would like to clean my Necchi Model 3355 myself, but don't know where to start. Help

They will only go in one way, they have to be correctly orientated.

https://www.google.com/search?q=Necchi+model+3355+replace+bobbin+case

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Question edited for clarity and all the typos.
Question moved from Televisions to make model category.

The whirling noise is the motor. It may be that the drive belt has broken?

When was the last time it was professionally cleaned, serviced and timed? With moderate use, they need doing every 2 to 3 years. The inside workings of sewing machines are very tough and seldom 'break'.

https://az589519.vo.msecnd.net/productdocuments/Inst-book-NECCHI-FA16.pdf

Parts including the $4.99 drive belt

https://www.sewingpartsonline.com/necchi-4575-sewing-machine-parts.aspx?index=32

Generic videos on Necchi belts

Hi,

Please add a bit of some olive oil (or similar oil) to shafts and areas of your machine that facilitate the selector's movement. This should lower friction and allow for movement.

Thank you.

It should set the width automatically when buttonhole is selected. Set the length to fine stitch.

Is the bobbin wheel actually turning? If so, the bobbin winder is still activated. Have you tried turning the inner wheel on the handwheel to de-activate the bobbin (see video)?

Amber Necchi Machine Basics

If that doesn't help, you may need to take the machine for service.

Manual:
https://www.manualslib.com/manual/940234/Necchi-534-Fb.html

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Be sure to try it with a brand new needle. If that doesn't work, then (as suggested), most likely the timing.

Necchi 537-L Sandi, Machine made in Taiwan, My guess on age would be early 80's. Links below may help, first link one lady states buy her 537L from sears in 1982., other links are instruction and info.
Check the attached links,instruction and guides, Good luck
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Life With Lou Necchi 537L Sewing Machine

Necchi 536 FB 537 FA Sewing Machine Threading Diagram

http://www.sewingpartsonline.com/necchi-sewing-machine-instruction-manuals.aspx

There could be a lot of reasons the hand wheel will not turn.Start with a good cleaning.My rule if it moves give it a lube. Usually a good cleaning will solve a lot of problems. If you are unsure owhre to oil let me know the machine model and I will try to help

I have the same machine and have had a similar problem. My belt was just old though. You need a new belt. And once installed it must be adjusted properly for everything to work correctly. I changed and adjusted mine myself. Although Necchi parts are not available from the company any more, there are several places online that carry belts and a few other items. One is sewingpartsonline.com. The belt shows up under Necchi 541, but it lists compatibility with our machines (549) on the order page. The size belt is 12 5/8"-- with teeth (lug type). While the belt is being changed the shaft that holds the wheel needs to be cleaned and oiled. Also clean up any excess oil in the area with a sewing machine safe cleaning fluid. Clean the plastic wheel with a little dish detergent and water on a paper towel. Oil should not be put, or remain, on any plastic parts in your machine. Not many people want to fix these machines anymore, but I love mine and will probably keep it as long as I can keep it running. Hope you see this post and get your machine running again. Win

i repair a lot of sewing machines as a hobby .. the necchi is one of the better ones .. they are easy to use and work well .. i almost always dontate the repaired machines to places like "womens shelter" .. "home for troubled girls" or just give them to someone that has nothing or cant afford new machines ... it sometimes makes a difference in their life if someone helps them get started .. modern machines vary from really cheap junkers that somehow work to really expensive machines that do everything but are completely out of reach for many.. the old necchis are better than many new machines but no one knows that .. so typically they sell for only $20 to $50 ... but if you donate a working machine to someone it can help, then its worth it weight in gold ..