The reason you and your friend are parsing this differently is that, as a written sentence, its semantics and its grammar go against each other. There are three main factors to why this is so:
1. Syntax/semantics of press
Crucial to why this is so is the syntactic-semantic properties of the verb press, which can be:
- intransitive (“She pressed harder and the stubborn button finally gave way”)
- transitive (“She pressed her nose against the glass”)
- unaccusative(-ish) (“Her nose pressed against the glass”)
Unaccusative verbs are intransitive syntactically, but differ from normal intransitives in that the subject is not the agent, and the agent is normally left unspoken; they are thus semantically closer to the transitive constructions than the intransitive constructions. Thus, “She pressed her nose against the glass” and “Her nose pressed against the glass” mean more or less the same thing, despite the sentences having different syntactic structures.
2. Morphological coalescence
English does not distinguish the simple past tense from the passive participle in regular verbs—both are pressed in this case. That is known as morphological coalescence, when two functionally distinct forms are identical in appearance.
The simple past, being a tense, is used as the main verb in clauses; you can substitute it for the simple present press(es), the present perfect has/have pressed, etc.
The passive participle, being a participle, is not used as the main verb in a clause, but it is used in various types of absolute constructions, i.e., phrases with no main verbs embedded in sentences, known as participial phrases. One common type of participial phrase has the basic structure
[possessive determiner] [possessee] [participle] [various other complements] and denotes a state or action that applies to the subject of the main clause while the action in the main clause takes place; for example:
He walked down the corridor, his head held high.
She ran up the stairs, her voice ringing out loud and clear.
He slouched into the room, his hands stuffed firmly in his pockets.
Distinct main clauses are generally separated by conjunctions, semicolons, or full stops (or exclamation marks, etc.) in English. Commas are used to bound off various types of subordinate clauses and often also absolute constructions, but should not, according to traditional rules of punctuation, be used to separate main clauses; doing so is what’s known as a comma splice.
Putting it together
The logical semantic properties of the passage in question here make it likely that the intended course of events is that ‘she’ (whoever she is) first ran towards the display and then, when she got there, pressed her nose to the glass. The punctuation (a simple comma with no conjunction), however, leads us to want to interpret the whole thing as one sentence, rather than two.
In many cases, this does not really create that much of a problem, because in many cases it’s simply not possible to interpret something as a single sentence. For example:
She ran towards the display, I pressed my nose against the glass
This is a comma splice, but it’s still quite unambiguous—there are two separate subjects and two separate main verbs, both with distinct further complements (“towards the display” in the first, “my nose” and “against the glass” in the second), so there must be two main clauses. There is no possible way to interpret either as some type of subordinate element of the other.
This is not the case with your sentence, though: “She ran towards the display” is a main clause, no doubt about it; but “her nose pressed against the glass” is syntactically ambiguous.
Because the simple past and the passive participle are identical and because press is one of those verbs that can be either transitive or unaccusative(-ish), two different interpretations are, on the face of it, equally valid:
- Active unaccusative clause: her nose pressed against the window = her nose was pressing up against the window
- Passive participial phrase: her nose pressed against the window = her nose being pressed up against the window [by her]
The former of these is a main clause; the latter a subordinate phrase. The former does not indicate any particular temporal relationship between itself and the preceding main clause (it can be simultaneous, or it can be sequential—depends on the context); the latter specifically encodes taking place simultaneously with the preceding main clause.
Now you see the problem with the latter half of the statement:
The comma and lack of conjunction leads us to read it as a subordinate phrase, which reading entails simultaneity; but the logic of the statement as a whole leans heavily towards sequentiality, which requires a main clause reading.
Conflict ensues, and you end up having to choose one or the other as a suboptimal compromise: you either let syntax and punctuation win (well-formed sentence, but doesn’t make sense), or you let semantics win (makes sense, but ill-formed sentence). You and your friend just chose different compromises.