There being no iron then,people had to use stone for making tools.怎样判断这句话中的being是做状语

前半句是现在分词作独立主格结构，做伴随状语，再根据前后意思判断，是做原因状语。
此句可改为 As there was no iron then,people had to use stone for making tools.
要注意的是，如果是两个句子的话需要加连词。
希望能帮到你，如有疑问，欢迎再提。

根据语境，相当于As there was no iron then,people had to use stone for making tools.
判断作何种状语，须根据语境而定。

There be 结构为非谓语形式时,be可以是不定式（to be）或（being）,there 作逻辑主语.非谓语形式的there to be 和there being 结构可用作主语、宾语、或状语.例如：There being a bus stop near the village is a great advantage .村庄旁边有个汽车站,真是方便极了.（作主语）We expect there to be no argument .我们希望不再出现争吵.（作宾语）There being no buses , we had to walk home .由于没有公共汽车了,我们只好步行回家.（做状语）There not being any water to drink , he fell rather thirsty .因为没有水喝,他感到很渴.（做状语）那么,什么时候用there to be,什么时候用there being呢?（一）、做主语1. 有for引导,则用there to be. It’s a great pity for there to be much trouble in the class. 太遗憾了,这个班上有多方面的麻烦. It is common for there to be problems of communication between teachers and students. 老师与学生人之间存在着沟通问题是很常见的.2. 没有for引导,则用there being.There being a public bus service is a great convenience to people. 公交车对人们十分方便.The * is heavily guarded. There being no hope of escape is certain.（二）、做动词的宾语① 跟动名词的动词后用there being.常见的动词有：deny, appreciate, mind, imagine, admit,② 跟不定式的动词后用there to be. 常见的动词有：want, expect, hope, wish, like , hate, would like, prefer, mean, intend等.She denied there being any misunderstanding between them.她否认他们之间有任何误会.　Teachers don’t want there to be any students lagging behind. 老师不希望有任何学生掉队.They hate there to be long queues everywhere. 他们不愿意处处都要排长队.（三）、做作状语 1. 作独立主格结构,用there being.There being nothing else to do, they went home.没有别的事做,他们回家了.There being nobody else to help me, I had to do by myself．由于没有人帮我,我只得单干了2. 但若置于介词for之后,则用there to be,整个介词短语作程度状语.It was too late for there to be any buses. 太晚了,不会有公共汽车了.

你看去掉逗号前面的整个句子there being no iron then，后面的是一句完整的句子，就说明是做状语的，主谓宾齐全。