It looks like the hinges are broken and bent, unsure what would cause that to happen. I'm not sure, but it doesn't look like there is a hinged part that Singer machines have once the machine is raised. Since you say it opened rather forcibly, I'm thinking that it may have been because as you lifted the top - it was also raising the machine head into position. I'm guessing that when you raised the top, that it also raised the machine and you didn't have to lift up the machine into position.
I wish someone who had a similar machine would chime in.
I think that if it were me I would replace the hinges if possible to find similar ones.
Janey - Neat people never make the exciting discoveries I do.