原来in your first two sentences are used to say that you are not surprised by something, I think people tend to use NO WONDER to express the same thing in English. (I can't think of any other English equalents at the moment. I'm afraid that there's no word for that in English.)
教室里怎么安静,原来人多走了。No wonder it's so quiet here, they're all gone.
怪不得他汉语说得怎么好,原来他妈妈是中国人。No wonder his Chinese is so good, his mother is Chinese.
原来 has a different meaning in your last two sentences, we use 原来 to talk about the situation before things changed or before other things happened.
原来我也想去的,因为有事儿没去成. I wanted to go, but something came up, so i didn't go. (原来 implies that your plan changed. )
这儿原来交通恨不方便,现在通了火车方便多了。the traffic was bad here, but now it's been improved since train lines came through this area。 (原来 implies that the traffic changed.)
我原来是工程师,现在是医生。I used to be an engineer, but now I am a doctor.(原来 implies that you changed your career.)
它原来是白的,现在是粉色了。it was white, it is pink now.(原来 implies that the color has been changed.)