I found a Singer 503a on my Birthday last year. I got her for $20 - no cams or feet. Door missing. It sews beautifully though. I gave it to my DIL to learn to sew. I asked her what she was going to name it. She thought and thought and finally said she was going to name her machine Margaret after her grandma. She was very fashionable in her day and she was a hard worker, very tough and sturdy built and she said she just loves her to bits even though she has parts missing.
You don't drop the feed dogs you raise the throat plate. Check your manual.