Rushing to the window, the fire enginees could be seen speeding down the street.

You need a different subject because it sounds like the fire engines were rushing to the window. Who was rushing to the window?

The fire engines should be the direct object in this sentence.

It reads like the fire engines are rushing to the window, so how would YOU change it? An observer (you, me, Aunt Matilda) needs to be in either the first or second part of the sentence. Give it a shot below.