In the sentence

 - *The player appears to have **not** connected.*

*connected* is the focus of negation, and thus *not* can appear directly before it, as here.

However, *not* can **also** appear directly before the beginning of any constituent containing its focus.

*Connected* is in the [Verb Phrase][1] *have connected*, so *not* can go before that, too

 - *The player appears to **not** have connected.*

and also in the [Infinitive Complement][2] *to have connected*, so *not* can go before that, too

 - *The player appears **not** to have connected.*

Since *appear* is a [Neg-Raising][3] verb (i.e, it's transparent to negation), *not* can **also** negate  
the complex VP constituent *appears to have been connected*. 

This, of course, requires *Do*-Support, because *appears* is present tense, and negating a tensed verb  
requires an auxiliary verb to carry the tense. When there's no auxiliary verb already in the tensed VP to be negated, one uses *Do*.  That's [*Do*-Support;][4] i.e,

 - *The player **does not** appear to have connected*,  
or, more likely
 - *The player **doesn't** appear to have connected*.

They're all grammatical, and they all mean the same thing.  
And I didn't even mention [A-Raising][5].


  [1]: http://www.umich.edu/~jlawler/VPguide.pdf
  [2]: http://www.umich.edu/~jlawler/Complements.pdf
  [3]: http://english.stackexchange.com/a/185419/15299
  [4]: http://english.stackexchange.com/a/78591/15299
  [5]: http://www.umich.edu/~jlawler/cliffs-equi-raising.pdf