I have one 35 year old 700 and one about 5 years old.
The older one is a 22-250 and if you want to shoot single shots or load the magazine and be able to shoot 5 shots, you must load the magazine and push the rounds back with your thumb if you want them to feed. Otherwise they want to jam.
If the feeding problem you described is what I think it might be, it may be a bad follower like one of my 700's. I called Remington and they sent me a new one, and the problem went away.