I was just thinking about how German appears to not make a distinction that is present in English (along with the well-known, I suppose, bit about not distinguishing between "The students, who study hard, will succeed" and "The students who study hard will succeed" since such clauses are always set off by commas in German).
Specifically, I make a distinction between "try to press the button" and "try pressing the button". For me, the first means something like "I don't think you can press the button, but feel free to prove me wrong" while the second is something like "I think you can press the button and believe that doing so may help you achieve your (unspecified) goal, so I encourage you to press it".
For, perhaps, a better explanation, consider the first thing that comes to mind when completing the sentence "He ____ the button, but...": I come up with something like "He tried to press the button, but couldn't reach it" and "He tried pressing the button, but nothing happened", respectively.
I think that in German both would be "Er versuchte, den Knopf zu drücken". (Though I might render "try pressing" with "Er versuchte es damit, den Knopf zu drücken".)
As for the third alternative in English, "try and press the button", I tend not to use it (possibly under the influence of my prescriptivist father's views on "proper English"), but I'd consider it equivalent to "try to press the button", rather than to "try pressing the button".