非谓语动词的使用，无非考虑三个方面。一是时间性，二是主动与被动性，三是动词的词性是动态还是静态。

就这个start来说，动词本身应该是动态的（可以商榷），动作应该是主语he的主动动作并且发生的时间应该在现在说话时刻之前。所以也可以用having started来强调动作，但也不排除用starting来强调一般的性质或状态的可能性。

所以我认为，用having started也可以，但用starting也不一定错。

Starting as a street vendor, he is now general manager of a trading corporation in Beijing.

我觉得句子没有错。《薄冰语法》认为句中的 Starting as a street vendor 是主语补语。

即原句相当于：

He started as a street vendor, and he is now general manager of a trading corporation in Beijing.

但我认为也可以看作让步状语，即原句相当于：

Though he started as a street vendor, he is now general manager of a trading corporation in Beijing.

个人看法，不妥之处请曹老师指正！

    我觉得薄冰教授的句子是正确的。start as = have an initial job as ...  关于这句话Starting as a street vendor, he is now general manager of a trading corporation inBeijing.说话人指的是最初的工作虽然是街头小贩, 但现在已经是总经理了。说话人并不是想强调先后的变化有什么关联。

请看国外报刊的例句,我们可以从中体会现在分词的用法：
Starting as a research assistant and advancing to her present position of associate counsel, she has played both minor and major roles in legal actions.

Starting as low as $75, packages are now available for the 2017/18 season of Arizona Opera.

Picking up his education in this way, Burchell made himself one of the world's authorities on bacteriology.

我觉得这里如果使用having started 反而不准确，不合乎逻辑。如：Have started as a street vendor, he is now general manager of a trading corporation in Beijing. 改后的这句话，会误认为因为开始当了小贩， 今天才能成为总经理。这显然不合乎逻辑。

    请看国外报刊的这个句子：Having started and owned two small businesses, I know what a challenge it is to keep up with the rising costs of your employees' healthcare premiums. 这里用having started是正确的，因为强调先后的关系，即开办了企业，才知道带来了一些问题。

所以我觉得认为主语补足语是可以接受的，如果说状语，也挺勉强，因为有时指方式，有时又不是。当然先有语言，后有语法，我个人认为学会正确使用就可以，至于语法成分怎么称呼，不是最重要的。

Starting as a street vendor看起来没有语法错误；

整句话意思：从一个街头小贩开始，他现在在北京是一个贸易公司的总经理。逻辑应该是没错误；

Starting as a street vendor是状语，不知什么状语？